ࡱ>  ~_ $bjbjzXzX X2@\2@\^+     4448l<46tT   "6$6$6$6$6$6$67:v$6  "   $6  96""" j  "6" "6"":45@ +vf46O6064; ;(5; 5D"   $6$6"   6    ;          > : Mr. Stump Algebra II W/ Trig Name:____________________ Quadratics Practice Test Topics, skills, and concepts to know: Factoring quadratics Finding a quadratic equation from given information: Vertex and one other point x-intercepts and one other point Any three points Graphing quadratic functions in normal, vertex, and factored form Changing from one form to another: Factored to normal (standard) Vertex to normal Normal to vertex (you need to complete the square) Normal to factored (you need to factor) Find the vertex of a quadratic function (you should know lots of ways!) Solving a quadratic equation (i.e. find the x-intercepts) Calculator Graphing Factoring (monic and nonmonic) Completing the square Quadratic formula Solving for the exact answers (in simplified radical form) of a quadratic function Deriving the quadratic formula Note: A major focus of this unit was learning multiple ways to solve problems. Part of your learning included knowing efficient solving techniques given certain situations. These questions are not intended to be sample test questions, nor should you assume that the material covered in these questions covers all the topics that you may be tested on. Review Questions These are application problems in which the vertex is an important point. Each problem specifies one or more methods for finding the vertex, so you get to practice all the methods. 1. The Gateway Arch is the centerpiece of the St. Louis skyline. Its shape is a parabola  Suppose the quadratic function describing this shape is F(x) =  EMBED Equation.3 , where x and F(x) are in feet. a. Find the zeros of F(x). b. Use the zeros to find the coordinates of the vertex & the line of symmetry. c. Sketch a graph of F(x). Label the zeros and the vertex with their coordinates. **SKIP** d. What is the appropriate interval of x-values for describing the Arch? e. Check your work so far by graphing F(x) =  EMBED Equation.3  on your calculator (you will need to set an appropriate window), then finding the maximum on your calculator. f. Visitors to the Arch can take a tram ride up to the top of the monument. How high above the ground is this? 2. You are selling cookies for a school club at a bake sale. Naturally, the higher you set the selling price, the fewer cookies you will sell. Suppose you will sell (500 4x) number of cookies at (x) cents per cookie. Let R(x) represent the total amount of money made from the cookie sale. Part A-D will ask you to determine the same information using different methods. a. Write a function formula for R(x). b. Find the zeros of R(x), then use the zeros to find the coordinates of the vertex. c. Rewrite the formula for R(x) in standard form, then use the conversions to find the coordinates of the vertex. d. Rewrite the formula for R(x) in vertex form, and use this to identify the vertex. e. On a graphing calculator, graph R(x) and find its vertex. f. You should have gotten the same x and y coordinates for the vertex from the first four parts of this problem. Do all your answers agree? g. What do the coordinates of the vertex tell you about the cookie sale? 3. a. Solve 2x2 + 4x + 6 = 0. b. Using conversions, put y = 2x2 + 4x + 6 into vertex form and find the vertex. c. Compare the calculations used for parts a and b. What steps were the same? What steps were different? 4. Suppose that (x k) is one of the factors of a quadratic function f(x). What else does this tell you about f(x) and its graph? What can you not discern from this information? Be specific. 5. Give an example of a quadratic whose zeros fit each description, or explain why you cant. a. only one real zero b. two real zeros c. three real zeros 6. Find a quadratic function whose zeros would be  EMBED Equation.3 & 3, and a y-intercept of 6. Give your answer in standard form. 7. Solve for x by using the conversions:  EMBED Equation.3  8. a. If you know the x-intercepts of a parabola, can you determine the vertex? Explain. b. If you know the x-intercepts of a parabola, can you determine the line of symmetry? Explain. 9. For a quadratic function y = ax2 + bx + c, under what circumstances would c represent both the y-intercept and the y-coordinate of the vertex? 10. Write an equation for a parabola that rises more steeply than y = x2 and has its vertex at (2, 5). 11. We studied three equation forms for quadratic functions: standard form, factored form, and vertex form. Using these three forms, write a set of three equations that all represent the same parabola. 12. Write a quadratic equation that has 2 distinct solutions that are: both integers both irrational 13. Solve by factoring: a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  f.  EMBED Equation.3  14. Suppose the equation  EMBED Equation.3  has roots  EMBED Equation.3  and  EMBED Equation.3 . Without solving the equation, find a quadratic equation with the following roots:  EMBED Equation.3  and  EMBED Equation.3 . Answers 1. a.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  e. window  EMBED Equation.3   EMBED Equation.3  f. 630 feet 2. a.  EMBED Equation.3  b-e.  EMBED Equation.3  f. 62.5 cents, make $15,625 3. a.  EMBED Msxml2.SAXXMLReader.5.0  b.  EMBED Msxml2.SAXXMLReader.5.0   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Msxml2.SAXXMLReader.5.0  4. If  EMBED Msxml2.SAXXMLReader.5.0  is a factor, then  EMBED Msxml2.SAXXMLReader.5.0  is an x-intercept of the graph (and a solution, zero, and root). You cannot discern if this is the only factor or if there is one other factor. You also dont know the leading coefficient, a. 5. Possible answers: a.  EMBED Msxml2.SAXXMLReader.5.0  b.  EMBED Msxml2.SAXXMLReader.5.0  c. Not possible. A quadratic has at most two real zeros. 6. a.  EMBED Msxml2.SAXXMLReader.5.0   EMBED Msxml2.SAXXMLReader.5.0   EMBED Msxml2.SAXXMLReader.5.0   EMBED Msxml2.SAXXMLReader.5.0   EMBED Msxml2.SAXXMLReader.5.0   EMBED Msxml2.SAXXMLReader.5.0   EMBED Msxml2.SAXXMLReader.5.0  7.  EMBED Msxml2.SAXXMLReader.5.0   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Msxml2.SAXXMLReader.5.0  8. a. Average the two x-intercepts to find the x-coordinate of the vertex. b. Average the two x-intercepts to find the line of symmetry. 9. When  EMBED Equation.3 , so when b = 0 10. Example:  EMBED Msxml2.SAXXMLReader.5.0  11. Factored: EMBED Equation.3  Normal: EMBED Equation.3  Vertex: EMBED Equation.3  12. a.  EMBED Equation.3 ,  EMBED Equation.3  b.  EMBED Equation.3 ,  EMBED Equation.3  13. a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  f.  EMBED Equation.3  14.  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Equation.39q-2 0 x=0x=420 FMicrosoft Equation 3.0 DS Equation Equation.39qOle UCompObjPRVfObjInfoSXEquation Native YM120 V(210,630) FMicrosoft Equation 3.0 DS Equation Equation.39q%2d0 0d"xd"420_1424099556OYVF + +Ole [CompObjUW\fObjInfoX^Equation Native _A_1424099589^[F + +Ole aCompObjZ\bf FMicrosoft Equation 3.0 DS Equation Equation.39q%2d0 0d"xd"420ObjInfo]dEquation Native eA_1424099605`F + +Ole gCompObj_ahfObjInfobjEquation Native kA_1424173424eF + + FMicrosoft Equation 3.0 DS Equation Equation.39q%20 0d"yd"630 FMicrosoft Equation 3.0 DS Equation Equation.39qOle mCompObjdfnfObjInfogpEquation Native q]AY W R(x)=x(500"4x)FMicrosoft EquationDNQE Equation.3ation.39q0  V(62.5,15_1298284995,jF + +Ole sCompObjiktfObjInfolvEquation Native wL_1424099022oiو=LlX + +Ole yCompObjnqzN625)FMicrosoft EquationDNQE Equation.3P P V @@hdxpr h, Symbol `.DMDM( "hObjInfo|OlePres000pr}x Ole10FmtProgID sEquation Native P currentpoint "(`-,Times)42)8x 8(52 `+4++,Times)H4);x)@+)D6)H=)H0/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2752 div 416 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (\000) 0 340 sh (\000) 848 340 sh (\000) 1630 340 sh (\000) 2190 340 sh /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute 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basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) 210 340 sh (\000) 1136 340 sh (\000) 1902 340 sh (\000) 2478 340 sh 224 ns (\000) 640 168 sh /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 432 340 sh (\000) 1374 340 sh end MTsave restore d@MATH4  -2x 2 +4x+6=0HXML.SAXReader.54  -2x 2 +4x+6=0FMicrosoft EquationDNQE E_1424099023viو=LlX + +Ole CompObjuxNObjInfoquation.3Z ZW @@dxpr , Symbol `.@Pb@Pb( " currentpoint ",Times(`y)H=)L-,Times)42)8x 8(5H2 `+4++)H4);x)@+)D6OlePres000wy Ole10FmtProgID zEquation Native P_1298436197}F + +/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2784 div 512 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 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round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put :newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000ertex ) -16 288 sh 384 /MT_Times-Roman f1 (\000) 1136 288 sh (\000) 1372 288 sh (\000) 1674 288 sh 384 /MT_Times-Roman f1 (\000) 1230 288 sh (\000) 1484 288 sh end MTsave restore d9MATH-   Vertex (1,8)XML.SAXReader.5-  Vertex (1,8)FMicrosoft EquationDNQE Equation.3Ole10FmtProgID AEquation Native BI_1424099035iو=LlX + +Ole DCompObjENObjInfoGOlePres000H Ole10FmtProgID s # @@hdxpr h, Symbol `.DSDS( "h currentpoint ",Times(P ()'x)D-,Times)Hk)0)/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1120 div 416 3 -1 roll exch div scale currentpoint translate 64 32 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put 9newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) -16 288 sh (\000) 892 288 sh /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 142 288 sh (\000) 702 288 sh 384 /Symbol f1 (\000) 414 288 sh end MTsave restore d$MATH6  (x-k)XML.SAXReader.5  (x-k)FMicrosoft EquationDNQE Equation.3Equation Native t4_1424099036iو=LlX + +Ole uCompObjvNObjInfoxOlePres000y2 Ole10FmtProgID Equation Native .  @@Xdxpr X, Symbol `.S0US0U( "X currentpoint ",Times(Px)H=,Times)Lk/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 896 div 352 3 -1 roll exch div scale currentpoint translate 64 32 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 16 288 sh (\000) 608 288 sh 384 /Symbol f1 (\000) 304 288 sh end MTsave restore dMATH  x=kXML.SAXReader.5  x=kFMicrosoft EquationDNQE Equation.3_1424099037iو=LlX + +Ole CompObjNObjInfoOlePres0000 Ole10FmtProgID Equation Native F_1424099038iو=LlX + + 9 @@dxpr , Symbol `.@Zm@Zm( " currentpoint ",Times(`y)H=,Times)H()'x)D-)D2)0) 8(52/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1824 div 512 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 16 340 sh (\000) 750 340 sh 384 /Symbol f1 (\000) 304 340 sh (\000) 1022 340 sh /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) 592 340 sh (\000) 1484 340 sh 384 /MT_Times-Roman f1 (\000) 1294 340 sh 224 ns (\000) 1628 168 sh end MTsave restore d6MATH*  y=(x-2) 2tXML.SAXReader.5*  y=(x-2) 2Ole CompObjNObjInfoOlePres000 FMicrosoft EquationDNQE Equation.3Z Z U @@hdxpr h, Symbol `.DJDJ( "h currentpoint ",Times(Hy    !"#$%&'()*+,-./0123456789:;<=>?@ABCFILMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{~)H=,Times)H()'x)D-)D2)0)()Gx)D-)H3)+)/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2720 div 416 3 -1 roll exch div scale currentpoint translate 64 0 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 16 288 sh (\000) 750 288 sh (\000) 1769 288 sh 384 /Symbol f1 (\000) 304 288 sh (\000) 1022 288 sh (\000) 2041 288 sh /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) 592 288 sh (\000\() 1484 288 sh (\000) 2503 288 sh 384 /MT_Times-Roman f1 (\000) 1294 288 sh (\000) 2329 288 sh end MTsave restore d9MATH-   y=(x-2)(x-3)XML.SAXReader.5-  y=(x-2)(x-3)FMicrosoft EquationDNQE EOle10FmtProgID  Equation Native  I_1424099040iو=LlX + +Ole CompObjNObjInfoOlePres000V Ole10FmtProgID Dquation.3. .[ @@xdxpr x, Symbol `.ix[ix[( "x currentpoint ",Times(Xy)H=,Times)La)/()(x)D- 8(21+>2":' `(X)()Gx)@+)H3),)/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2912 div 480 3 -1 roll exch div scale currentpoint translate 64 32 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1516 208 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict y{ exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 16 320 sh (\000) 608 320 sh (\000) 956 320 sh (\000) 1975 320 sh 384 /Symbol f1 (\000) 304 320 sh (\000) 1228 320 sh (\000) 2231 320 sh /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) 798 320 sh (\000\() 1690 320 sh (\000) 2693 320 sh 224 /MT_Times-Roman f1 (\000) 1540 168 sh (\000) 1548 416 sh 384 ns (\000) 2519 320 sh end MTsave restore dJMATH> u  y=a(x- 12 )(x+3)XML.SAXReader.5>  y=a(x- 12 )(x+3)Equation Native EZ_1424099042iو=LlX + +Ole GCompObjHNFMicrosoft EquationDNQE Equation.3 X @@xdxpr x, Symbol `.ixS0ixS0( "x currentpoint ",Times(X 6)H=,Times)La)/() 0)D- 8(ObjInfoJOlePres000K> Ole10FmtProgID |Equation Native }Z21+>2":{' `(X)()?0)@+)H3),)/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2816 div 480 3 -1 roll exch div scale currentpoint translate 64 32 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1452 208 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict z{ exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) -16 320 sh (\000) 892 320 sh (\000) 1879 320 sh (\000) 2423 320 sh 224 ns (\000) 1476 168 sh (\000) 1484 416 sh 384 /Symbol f1 (\000) 272 320 sh (\000) 1164 320 sh (\000) 2135 320 sh /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 576 320 sh 384 /MT_Times-Roman f1 (\000) 766 320 sh (\000\() 1626 320 sh (\000) 2597 320 sh end MTsave restore dJMATH>   6=a(0- 12 )(0+3)XML.SAXReader.5>  6=a(0- 12 )(0+3)_1424099044iو=LlX + +Ole CompObjNObjInfoFMicrosoft EquationDNQE Equation.3 * @@xPdxpr xP, Symbol `.ixHZixHZ( "xP currentpoint ",Times(X 6)H=)L-,Times 8(23*>2":' `OlePres000H Ole10FmtProgID Equation Native B_1424099046iو=LlX + + (Xa/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1344 div 480 3 -1 roll exch div scale currentpoint translate 64 32 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 832 208 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) -16 320 sh 224 ns (\000) 864 168 sh (\000) 864 416 sh 384 /Symbol f1 (\000) 272 320 sh (\000) 576 320 sh /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 1056 320 sh end MTsave restore d2MATH&  6=- 32 aXML.SAXReader.5&  6=- 32 aFMicrosoft EquationDNQE Equation.3Ole CompObjNObjInfoOlePres000 Z Z # @@Pdxpr P, Symbol `.}S}S( "P currentpoint ",Times(Ha)H=)L-,Times)44/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1120 div 320 3 -1 roll exch div scale currentpoint translate 64 0 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put %newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 0 288 sh 384 /Symbol f1 (\000) 288 288 sh (\000) 592 288 sh /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) 802 288 sh end MTsave restore d!MATHI  a=-4XML.SAXReader.5  a=-4FMicrosoft EquationDNQE Equation.3Ole10FmtProgID Equation Native 1_1424099048iو=LlX + +Ole CompObjNObjInfoOlePres000l Ole10FmtProgID D Db @@xdxpr x, Symbol `.ixrixr( "x currentpoint ",Times(Xy)H=)L-,Times)44)4()'x)D- 8(21+>2":' `(X)()Gx)@+)H3)+)/MTsave save def 40 dict beg      #$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUX[^_`abcdefghijklmnopqrstuvwxyz{|}~in currentpoint 3 -1 roll sub neg 3 1 roll sub 3136 div 480 3 -1 roll exch div scale currentpoint translate 64 32 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1742 208 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 16 320 sh (\000) 1182 320 sh (\000) 2201 320 sh 384 /Symbol f1 (\000) 304 320 sh (\000) 608 320 sh (\000) 1454 320 sh (\000) 2457 320 sh /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) 818 320 sh (\000) 2745 320 sh 224 ns (\000) 1766 168 sh (\000) 1774 416 sh 384 /MT_Times-Roman f1 (\000) 1024 320 sh (\000\() 1916 320 sh (\000) 2919 320 sh end MTsave restore dMMATHA   y=-4(x- 12 )(x+3)anXML.SAXReader.5A  y=-4(x- 12 )(x+3)FMicrosoft EquationDNQE EEquation Native ]_1424099050iو=LlX + +Ole CompObjNquation.3 ` @@dxpr , Symbol `.@l@l( " currentpoint ",Times(`y)H=)L-,Times)44)4()'x 8(5k2 `+4++ 8(:5*>2"B' `ObjInfo!OlePres000" Ole10FmtProgID VEquation Native Wr(`#x)D- 8(:3*>2"B' `(`)/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3072 div 512 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1886 228 rndmvto 160 0 rlineto stroke 2686 228 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 16 340 sh (\000) 1182 340 sh (\000) 2126 340 sh 384 /Symbol f1 (\000) 304 340 sh (\000) 608 340 sh (\000) 1598 340 sh (\000) 2398 340 sh /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) 818 340 sh 224 ns (\000) 1390 168 sh (\000) 1918 188 sh (\000) 1918 436 sh (\000) 2718 188 sh (\000) 2718 436 sh 384 /MT_Times-Roman f1 (\000) 1024 340 sh (\000) 2860 340 sh end MTsave restore dbMATHV w  y=-4(x 2 + 52 x- 32 )XML.SAXReader.5V  y=-4(x 2 + 52 x- 32 )FMicrosoft EquationDNQE Equation.3` `\ @@dxpr , Symbol `.@_@_( "_1424099052iو=LlX + +Ole YCompObjZNObjInfo\OlePres000] Ole10FmtProgID Equation Native S_1424099054iو=LlX- +- + currentpoint ",Times(`y)H=)L-,Times)44)<x 8(5L2 `+8+-)<10)gx)@+)D6/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2944 div 512 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 16 340 sh (\000) 1056 340 sh (\000) 2142 340 sh 384 /Symbol f1 (\000) 304 340 sh (\000) 608 340 sh (\000) 1488 340 sh (\000) 2398 340 sh /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) 818 340 sh (\0000) 1728 340 sh (\000) 2670 340 sh 224 ns (\000) 1264 168 sh end MTsave restore dCMATH7   y=-4x 2 -10x+6XML.SAXReader.57  y=-4x 2 -10x+6Ole CompObjNObjInfoOlePres000P FMicrosoft EquationDNQE Equation.3( ( Q @@hdxpr h, Symbol `.D@D@( "h currentpoint ",Times(` 2)7x 8(5w2 `+4++,Times)Hkx)o-)Hm)`=)H0/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2592 div 416 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis /Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Roman /MT_Times-Roman ref 384 /MT_Times-Roman f1 (\000) -16 340 sh (\000) 2312 340 sh 224 ns (\000) 414 168 sh /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 206 340 sh (\000x) 910 340 sh (\000) 1640 340 sh 384 /Symbol f1 (\000) 622 340 sh (\000) 1352 340 sh (\000) 2024 340 sh end MTsave restore d=MATH1  2x 2 +kx-m=0XML.SAXReader.51  2x 2 +kx-m=0FMicrosoft EquationDNQE Equation.3Ole10FmtProgID Equation Native M_1298286128 F- +- +Ole CompObjNObjInfoEquation Native f_1298286344hF- +- +J  x 2 + k2 x- m2 =0FMicrosoft EquationDNQE Equation.3  x 2 + k2 x+ k 2 16 - k Ole CompObjNObjInfoEquation Native 2 16 - m2 =0FMicrosoft EquationDNQE Equation.3  x+ k4 () 2 - k 2 16 + m2 ()=0_1298286357 F- +- +Ole CompObj  NObjInfo Equation Native _1298286262F- +- +Ole CompObjNFMicrosoft EquationDNQE Equation.3  x+ k4 +  k 2 +8m16 ()x+ k4 -  k 2 +8m16 ()=0ObjInfoEquation Native _1424099059iو=LlX- +- +Ole FMicrosoft EquationDNQE Equation.3LLA @@dxpr , Symbol `.k,C k,C ( " currentpoint ",Times(xxCompObjNObjInfoOlePres000tOle10FmtProgID       #&),-./0123456789:;<=>?@ABEHKLMNOPQRSTUVWXYZ[\]^_`adgjklmnopqrstuvwxyz{|}~)H= 8(M-,Times)#k) )Mk ((4`2 8+ +)$8) m"6# "Q, ! (B4 ZZ/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2080 div 608 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def /sqr { 1.5 mul 3 index div 6 1 roll gsave translate dup dup neg scale 4 -1 roll 2 div rnddist 2 mul /thick exch def dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .34 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .34 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 868 284 224 1054 284 9 sqr 16 th 608 324 rndmvto 1346 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def /mt_vec StandardEncoding 256 array copy def /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis mt_vec 128 32 getinterval astore pop mt_vec dup 176 /brokenbar put dup 180 /twosuperior put dup 181 /threesuperior put dup 188 /onequarter put dup 190 /threequarters put dup 192 /Agrave put dup 201 /onehalf put dup 204 /Igrave put pop /Egrave/Ograve/Oacute/Ocircumflex/Otilde/.notdef/Ydieresis/ydieresis 8/Ugrave/Uacute/Ucircumflex/.notdef/Yacute/thorn mt_vec 209 14 getinterval astore pop mt_vec dup 228 /Atilde put dup 229 /Acircumflex put dup 230 /Ecircumflex put dup 231 /Aacute put dup 236 /Icircumflex put dup 237 /Iacute put dup 238 /Edieresis put dup 239 /Idieresis put dup 253 /yacute put dup 254 /Thorn put pop /re_dict 4 dict def /ref { re_dict begin /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup dup /FID ne exch /Encoding ne and { exch newfont 3 1 roll put } { pop pop } ifelse } forall newfont /FontName newfontname put newfont /Encoding mt_vec put newfontname newfont definefont pop end } def /Times-Italic /MT_Times-Italic ref 384 /MT_Times-Italic f1 (\000) 16 436 sh 224 ns (\000) 782 266 sh (\000) 1218 266 sh (\000) 1744 266 sh 384 /Symbol f1 (\000) 304 436 sh 224 ns (\000) 640 266 sh (\000) 910 266 sh (\000) 1474 266 sh /Times-Roman /MT_Times-Roman ref 160 /MT_Times-Roman f1 (\000) 1346 166 sh 224 ns (\000) 1618 266 sh (\000) 1225 532 sh end MTsave restore dTMATHH _  x= -k k 2 +8m  4XML.SAXReader.5H  x= -k kEquation Native d_1298437487F- +- +Ole !CompObj"N 2 +8m  4FMicrosoft EquationDNQE Equation.3,  x= -b2a =0ObjInfo$Equation Native %H_1424099060J iو=LlX- +- +Ole 'CompObj"(NObjInfo*OlePres000!#+Ole10FmtProgID $CFMicrosoft EquationDNQE Equation.3P @@dxpr  , Symbol `.@}@}( " currentpoint ",Times(`y)D=,Times)H2)/()(x)@-)D2)/) 8(52 `+4++)H5/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2560 div 512 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (y) 16 340 sh (x) 924 340 sh 384 /Symbol f1 (=) 288 340 sh (-) 1180 340 sh (+) 1994 340 sh 384 /Times-Roman f1 (2) 576 340 sh (2) 1452 340 sh (5) 2282 340 sh 224 ns (2) 1786 168 sh 384 /Times-Roman f1 (\() 766 340 sh (\)) 1642 340 sh end MTsave restore d@MATH4 y=2(x-2) 2 +5 Equation.34 y=2(x-2) 2 +5FMicrosoft EquationDNQE EEquation Native DP_1424099061'F- +- +Ole FCompObj&)GNquation.3 U @@hdxpr  h, Symbol `.DJDJ( "h currentpoint ",Times(Hy)D=,Times)H()'x)@-)D2)0)()Gx)@-)H4)3)/MTsave saveObjInfoIOlePres000(*JOle10FmtProgID +bEquation Native cI def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2720 div 416 3 -1 roll exch div scale currentpoint translate 64 0 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (y) 16 288 sh (x) 734 288 sh (x) 1737 288 sh 384 /Symbol f1 (=) 288 288 sh (-) 990 288 sh (-) 1993 288 sh 384 /Times-Roman f1 (\() 576 288 sh (\)\() 1452 288 sh (\)) 2487 288 sh 384 /Times-Roman f1 (2) 1262 288 sh (4) 2281 288 sh end MTsave restore d9MATH-  y=(x-2)(x-4)o Equation.3- y=(x-2)(x-4)FMicrosoft EquationDNQE Equation.3_1424099062%3.F- +- +Ole eCompObj-0fNObjInfoh~~I @@Hdxpr  H, Symbol `.@^@^( "H currentpoint ",Times(`y)D=,Times)Px 8(52 `+4+-)D6)7x)@+)H8/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 233OlePres000/1iOle10FmtProgID 2Equation Native J_14240990635F- +- +6 div 512 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (y) 16 340 sh (x) 608 340 sh (x) 1518 340 sh 384 /Symbol f1 (=) 288 340 sh (-) 1024 340 sh (+) 1774 340 sh 224 /Times-Roman f1 (2) 816 168 sh 384 ns (6) 1296 340 sh (8) 2062 340 sh end MTsave restore d:MATH. y=x 2 -6x+8 Equation.3. y=x 2 -6x+8FMicrosoft EquationDNQE Equation.3H @Ole CompObj47NObjInfoOlePres00068@@dxpr  @, Symbol `.@[ @[ ( "@ currentpoint ",Times(`y)D=,Times)H()'x)@-)H3),) 8(52 `+4+-)<1/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2304 div 512 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (y) 16 340 sh (x) 734 340 sh 384 /Symbol f1 (=) 288 340 sh (-) 990 340 sh (-) 1804 340 sh 384 /Times-Roman f1 (\() 576 340 sh (\)) 1452 340 sh 384 /Times-Roman f1 (3) 1278 340 sh (1) 2044 340 sh 224 ns (2) 1596 168 sh end MTsave restore d=MATH1) y=(x-3) 2 -1 Equation.3Ole10FmtProgID 9Equation Native M_1424099069,V<F- +- +Ole 1 y=(x-3) 2 -1FMicrosoft EquationDNQE Equation.3 U @@hdxpr  h, SymCompObj;>NObjInfoOlePres000=?Ole10FmtProgID @bol `.DJDJ( "h currentpoint ",Times(Hy)D=,Times)H()'x)@-)H3),)()Gx)@-)H4)3)/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2720 div 416 3 -1 roll exch div scale currentpoint translate 64 0 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (y) 16 288 sh (x) 734 288 sh (x) 1737 288 sh 384 /Symbol f1 (=) 288 288 sh (-) 990 288 sh (-) 1993 288 sh 384 /Times-Roman f1 (\() 576 288 sh (\)\() 1452 288 sh (\)) 2487 288 sh 384 /Times-Roman f1 (3) 1278 288 sh (4) 2281 288 sh end MTsave restore d9MATH-  y=(x-3)(x-4)fo Equation.3- y=(x-3)(xEquation Native I_1424099070CF- +- +Ole CompObjBEN-4)FMicrosoft EquationDNQE Equation.3 % @@`(dxpr  `(, Symbol `.lblb( "`( ObjInfoOlePres000DFOle10FmtProgID GEquation Native 4currentpoint ",Times(Hx)D=,Times)L3)',) 4/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1184 div 384 3 -1 roll exch div scale currentpoint translate 64 0 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (x) 16 288 sh 384 /Symbol f1 (=) 288 288 sh 384 /Times-Roman f1 (3) 592 288 sh (4) 878 288 sh 384 /Times-Roman f1 (,) 750 288 sh end MTsave restore d$MATH x=3,4 Equation.3 x=3,4FMicrosoft EquationDNQE Equation.3_1424099073AOJF- +- +Ole CompObjILNObjInfoOlePres000KMLOle10FmtProgID NEquation Native A_1424099074QF- + T +$$1 @@dxpr  , Symbol `.@r@r( " currentpoint ",Times(`y)D=,Times)Px 8(52 `+4+-)H3/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1568 div 512 3 -1 roll exch div scale currentpoint translate 64 44 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (y) 16 340 sh (x) 608 340 sh 384 /Symbol f1 (=) 288 340 sh (-) 1024 340 sh 224 /Times-Roman f1 (2) 816 168 sh 384 ns (3) 1312 340 sh end MTsave restore d1MATH%` y=x 2 -3 Equation.3% y=x 2 -3FMicrosoft EquationDNQE Equation.3XX+ @@xXdxpr  xX, Symbol `.ixMixM( "xX Ole CompObjPSNObjInfoOlePres000RT     "#$%&'()*+,-./012345678;>ABCDEFGHIJKLMNOPQRSTUVWZ]`abcdefghijklmnopqrsty|}~currentpoint ",Times(hx)D=)H,Times)|3"I#-"o#4/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1376 div 480 3 -1 roll exch div scale currentpoint translate 64 48 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def /sqr { 1.5 mul 3 index div 6 1 roll gsave translate dup dup neg scale 4 -1 roll 2 div rnddist 2 mul /thick exch def dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .34 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .34 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 452 400 384 814 400 16 sqr /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (x) 16 368 sh 384 /Symbol f1 (=) 288 368 sh (\261) 576 368 sh 384 /Times-Roman f1 (3) 1074 368 sh end MTsave restore d*MATH x= 3  Equation.3 x= 3 FMicrosoft EquationDNQE Equation.3Ole10FmtProgID UEquation Native :_1424099075HdXF T + T +Ole CompObjWZNObjInfo OlePres000Y[!Ole10FmtProgID \93 @@dxpr  , Symbol `.@@@@( " currentpoint ",Times(Xx)D=)H-,Times 8(61+>2">' `(X,)-)43R/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1632 div 512 3 -1 roll exch div scale currentpoint translate 64 48 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 832 208 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (x) 16 304 sh 384 /Symbol f1 (=) 288 304 sh (-) 576 304 sh (-) 1136 304 sh 224 /Times-Roman f1 (1) 856 168 sh (2) 864 416 sh 384 ns (3) 1346 304 sh 384 /Times-Roman f1 (,) 1024 304 sh end MTsave restore d8MATH,b x=- 12 ,-3es Equation.3, x=- 12 ,-3FMicrosoft EquationDNQE Equation.3Equation Native :H_1424099076_F T + T +Ole <CompObj^a=NObjInfo?OlePres000`b@Ole10FmtProgID cXEquation Native YH3 @@dxpr  , Symbol `.@@@@( " currentpoint ",Times(Xx)D=)H-,Times 8(62*>5">' `(X,)-)43R/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1632 div 512 3 -1 roll exch div scale currentpoint translate 64 48 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 832 208 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (x) 16 304 sh 384 /Symbol f1 (=) 288 304 sh (-) 576 304 sh (-) 1136 304 sh 224 /Times-Roman f1 (2) 864 168 sh (5) 864 416 sh 384 ns (3) 1346 304 sh 384 /Times-Roman f1 (,) 1024 304 sh end MTsave restore d8MATH,f x=- 25 ,-3    Zz !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXY[]^_`abcdefghijklmnopqrstuvwxy Equation.3, x=- 25 ,-3FMicrosoft EquationDNQE Equation.3JJ @_1424099077]rfF T + T +Ole [CompObjeh\NObjInfo^OlePres000gi_rOle10FmtProgID juEquation Native v;_1424099078mF T + T +@dxpr  , Symbol `.@L@L( " currentpoint ",Times(Xx)D=,Times 8(63*>2">'/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 864 div 512 3 -1 roll exch div scale currentpoint translate 64 48 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 592 208 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (x) 16 304 sh 384 /Symbol f1 (=) 288 304 sh 224 /Times-Roman f1 (3) 624 168 sh (2) 624 416 sh end MTsave restore d+MATH x= 32 Equation.3 x= 32Ole wCompObjloxNObjInfozOlePres000np{FMicrosoft EquationDNQE Equation.3% @@(dxpr  (, Symbol `.@b@b( "( currentpoint ",Times(Xx)D=,Times 8(611+>7">7 `(X,)12/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1184 div 512 3 -1 roll exch div scale currentpoint translate 64 48 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 592 208 rndmvto 224 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (x) 16 304 sh 384 /Symbol f1 (=) 288 304 sh 224 /Times-Roman f1 (11) 592 168 sh (7) 656 416 sh 384 ns (1) 928 304 sh 384 /Times-Roman f1 (,) 848 304 sh end MTsave restore d5MATH) x= 117 ,1 Equation.3) x= 117 ,1FMicrosoft EquationDNQE EOle10FmtProgID qEquation Native E_1424099079kytF T + T +Ole CompObjsvNObjInfoOlePres000uwOle10FmtProgID xquation.3bb" @@dxpr  , Symbol `.@L@L( " currentpoint ",Times(Xx)D=)H-,Times 8(65*>3">'/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 512 3 -1 roll exch div scale currentpoint translate 64 48 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 832 208 rndmvto 160 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (x) 16 304 sh 384 /Symbol f1 (=) 288 304 sh (-) 576 304 sh 224 /Times-Roman f1 (5) 864 168 sh (3) 864 416 sh end MTsave restore d.MATH"; x=- 53 Equation.3" x=- 53FMicrosoft EquationDNQE Equation.3LL @Equation Native >_1424099080{F T + T +Ole CompObjz}NObjInfoOlePres000|~tOle10FmtProgID Equation Native ;@dxpr  , Symbol `.@L@L( " currentpoint ",Times(Xx)D=,Times 8(63(t4">+/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 864 div 512 3 -1 roll exch div scale currentpoint translate 64 48 translate /rndpos { transform round exch round exch itransform } def /rndvec { dtransform round exch round exch idtransform } def /rnddist { 0 rndvec pop } def /rndmvto { rndpos moveto } def /rndlnto { rndpos lineto } def /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 592 208 rndmvto 176 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (x) 16 304 sh 384 /Symbol f1 (=) 288 304 sh 224 /Times-Roman f1 (3) 632 168 sh (4) 624 416 sh end MTsave restore d+MATH x= 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