ࡱ> pr of|7 !bjbjUU 7|7|^lfff8*Ra:P(((```````$b (d`('(((`: a:::(L 8`:(`::1?RY[. ==2pf2 Z["a0Ra+Zd4d[:CHAPTER 4 TEST C Name: ___________________________ Directions: Show all work. Section: __________________________ Which one of the following graphs represents EMBED Equation.DSMT4 Which of the following equations has intercepts at EMBED Equation.DSMT4 ? EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4 Which one of the following gives an equation for the parabola shown?  EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4 The parabolaEMBED Equation.DSMT4 whose coefficients fit the system of equations at right contains which one of the following sets of points? EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4Which one of the following equations results from combining the equations in the system EMBED Equation.DSMT4 ? EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4 Which of the following intervals gives the solution to the inequality EMBED Equation.DSMT4? EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4 For problems 7-10, find the coordinates of the intercepts and the vertex of the parabola whose equation is given, then sketch a graph. EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 In problems 11-13, write an equation for the parabola passing through the origin EMBED Equation.DSMT4 and having its vertex at the given point. Sketch a graph for each showing the coordinates of all intercepts. EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 Solve the system of equations algebraically and verify your solutions with a graph. EMBED Equation.DSMT4 Solve the inequality: EMBED Equation.DSMT4. Write the solution in interval notation. Solve the inequality: EMBED Equation.DSMT4. Write the solution in interval notation. The area of the shaded region shown at right is formed by subtracting the area of a circle with radius r from the area of a square with edge s: EMBED Equation.DSMT4. Show that if the edge of the square is 8 less than 3 times the radius of the circle, then the area of the shaded region is EMBED Equation.DSMT4. Find exact values for r and s in problem #17 to produce a shaded region of area 60. Simplify the radicals in your expressions. The sum of half one number and one third of another number is 4. Find two such numbers so that their product is maximized. Salt water is entering a tank full of water at the same time that the water is draining out of the tank. The water is draining out of the tank at a faster rate than the water is coming in so that the total amount of salt in the tank, S, (measured in grams) at time t (measured in hours) is given by the quadratic equation, EMBED Equation.DSMT4. After how many hours is the amount of salt in the tank at a maximum? Approximate the solutions to EMBED Equation.DSMT4, accurate to the nearest hundredth. Approximate the solution interval to EMBED Equation.DSMT4 where r is positive. Round to the nearest hundredth in the solution interval. Approximate the x-intercepts of the parabola described by EMBED Equation.DSMT4. Temperature data for the years 1986 - 1990 taken from the middle of the Bay mouth (degrees Celsius)Month19861987198819891990Jan.5.285.521.565.765.28Feb.3.723.604.685.287.20Mar.5.765.287.205.889.72April10.909.8411.4011.5012.50May15.8017.6017.3016.7018.40June21.6020.4021.8022.5021.20July25.6024.4024.7026.0025.10Aug.25.1025.9022.8025.1026.30Sept.22.4024.4021.6022.7024.00Oct.20.0016.9018.0018.2021.10Nov.13.4012.6012.8013.6013.00Dec.9.366.969.727.708.64For problems 24 and 25, use the Chesapeake Bay temperature data tabulated at right. Use linear regression to find the best linear fit for the temperature during June in terms of the number of years since 1986. Use quadratic regression to find the best quadratic fit for the temperature during 1988 in terms of the number of months since the beginning of the year. Solutions For Chapter 4 Test Form C. cccedb The intercepts of EMBED Equation.DSMT4 are EMBED Equation.DSMT4. The vertex is at EMBED Equation.DSMT4. The intercepts of EMBED Equation.DSMT4 are EMBED Equation.DSMT4 The vertex is at EMBED Equation.DSMT4. The intercepts of EMBED Equation.DSMT4 are EMBED Equation.DSMT4. The vertex is at EMBED Equation.DSMT4. The intercepts of EMBED Equation.DSMT4 are EMBED Equation.DSMT4. The vertex is at EMBED Equation.DSMT4. Plugging EMBED Equation.DSMT4 into EMBED Equation.DSMT4, shows that EMBED Equation.DSMT4. If the vertex is at EMBED Equation.DSMT4, then EMBED Equation.DSMT4. The parabola EMBED Equation.DSMT4, has another intercept at EMBED Equation.DSMT4. EMBED Equation.DSMT4EMBED Equation.DSMT4 gives an equation for the parabola. 0ther intercept at EMBED Equation.DSMT4. Again, EMBED Equation.DSMT4 yields EMBED Equation.DSMT4 as an equation for the parabola. The other intercept is at EMBED Equation.DSMT4. Substituting EMBED Equation.DSMT4 into EMBED Equation.DSMT4 we have EMBED Equation.DSMT4 This is equivalent to EMBED Equation.DSMT4 so that EMBED Equation.DSMT4. Computing the corresponding y-values, we find solutions at EMBED Equation.DSMT4 and EMBED Equation.DSMT4, as shown: EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4 EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4. Substituting EMBED Equation.DSMT4 into EMBED Equation.DSMT4 EMBED Equation.DSMT4, we have EMBED Equation.DSMT4. EMBED Equation.DSMT4EMBED Equation.DSMT4 EMBED Equation.DSMT4EMBED Equation.DSMT4. But if EMBED Equation.DSMT4, then EMBED Equation.DSMT4, which is impossible. So EMBED Equation.DSMT4 and EMBED Equation.DSMT4 Let EMBED Equation.DSMT4 represent the two numbers. Then EMBED Equation.DSMT4 so that the product is EMBED Equation.DSMT4. This expression is maximized where EMBED Equation.DSMT4 EMBED Equation.DSMT4. Thus the numbers we seek are EMBED Equation.DSMT4 and 6. EMBED Equation.DSMT4 is maximized where EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 and EMBED Equation.DSMT4 if EMBED Equation.DSMT4 (see #21.) EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  Above is shown how a TI85 calculator could be programmed to find these solutions. Note that the discriminant , D, is computed. The screen shots below show how the linear regression is carried out on a TI-85. This process varies quite a bit from calculator to calculator. The third screen is interpreted to show the regression line is EMBED Equation.DSMT4 .  Screen shots for quadratic regression are shown below. The regression parabola fitting temperature to time (in months) is EMBED Equation.DSMT4.  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