2.8 graphs of factorable polynomials t
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This document discusses how to graph factorable polynomials by identifying the roots and their orders from the polynomial expression, making a sign chart, sketching the graph around each root based on the order, and connecting the pieces to obtain the full graph. As an example, it identifies the roots x=0, x=-2, and x=3 of order 1, 2, and 2 respectively from the polynomial P(x)=-x(x+2)2(x-3)2, makes the sign chart, and sketches the graph around each root to ultimately connect them into the full graph of P(x).
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2.8 graphs of factorable polynomials t
- 1. Graphs of Factorable Polynomials For example, given two roots with their orders and the sign-chart of a polynomial, the graphs around each root are as shown. Connect them to get the whole graph. Example C. Given P(x) = -x(x + 2)2(x – 3)2, identify the roots and their orders. Make the sign-chart. Sketch the graph about each root. Connect them to complete the graph. The roots are x = 0 of order 1, x = -2 of order 2, and x = 3 of order 2. + order=2 order=3
- 2. Graphs of Factorable Polynomials The sign-chart of P(x) = -x(x + 2)2(x – 3)2 is x = -2 order 2 ++ x = 0 order 1 x = 3 order 2 By the sign-chart and the order of each root, we draw the graph about each root. (Note for x = 0 of order 1, the graph approximates a line going through the point.) Connect all the pieces to get the graph of P(x).