ࡱ>  N bjbjWW 455N||Q^ppppKKK$IKKKKKpp iiiKppiKii0p4T a:!0Q,00KKiKKKKK#FKKKQKKKKKKKKKKKKK| :  Summary for Polynomial Functions FTA (Fundamental Theorem of Algebra) A polynomial of degree n must have n roots. Roots can be real numbers or imaginary numbers or a combination of both. For real polynomials i.e., polynomials with Integer coefficients, imaginary roots always come in pairs. For graphing polynomial functions, use the strategy outlined in class; (on my web page). Features of Graphs of Polynomial Functions The end behavior of the function, i.e., as  EMBED Equation.3 , is governed by  EMBED Equation.3 ( the term of the highest order). If the multiplicity of the root is even then the graph touches the x-axis. If the multiplicity of the root is odd, then the graph crosses the x-axis. The number of turns in the graph of a polynomial function is at most ( EMBED Equation.3  ) n 1. T.F.A.E. (The Following Are Equivalent) If x =r is a root for a polynomial P(x) then: P(r) = 0 (x-r) is a factor for P(x) x=r is a zero for P(x), i.e. it is the value that makes P(x) =0 (r,0) is an x-intercept for the graph of P(x) So for example : The answer is x= -2 , 1 3i. Find the polynomial of lowest power that has the above listed roots. Take  EMBED Equation.3  Solution: Since 1 3i is a root, then its conjugate must also be a root. This means 1+3i is also a root.  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