Lesson 5.8 Graphing Polynomials.

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Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

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Presentation transcript:

Lesson 5.8 Graphing Polynomials

Steps A) Find the roots or zeros (factor if necessary) B) Find the y-intercept (let x = 0) C) Determine the end behavior D) Check to see if it “bounces” E) Sketch the graph

Graph 1. f(x) = (x + 2)(x – 3)(x – 1)

2. f(x) = .5(x + 3)2 (x – 2)2

3. f(x) = -x2(x – 1)(x + 4)

4. f(x) = -2x3 – 2x2 + 40x

5. f(x) = x3 + 5x2 – 4x – 20

6. f(x) = x4 - 10x2 + 9

A turning point is where a graph changes from increasing to decreasing or vice versa. Identify the turning points on the last graph. Estimate the coordinates. Determine whether they are minimum or maximum values. How many turning points did the graph have? How did this compare to the degree of the graph?

We already know that a polynomial of degree n can have AT MOST n real zeros. n-1 turning points.