HW Friday (due Monday): Pre-Calculus Honors Zeros of a function HW Friday (due Monday): 2.2: p.110 (38-44 even, 52, 56, 74, 80, 86-92 even) Copyright © Cengage Learning. All rights reserved.

Zeros of Polynomial Functions What are zeros of a function? A zero of a function f is a number x for which f (x) = 0. It can be shown that for a polynomial function f of degree n, the following statements are true. 1. The function f has at most n real zeros. 2. The graph of f has at most n – 1 relative extrema (relative minima or maxima).

2.2: Finding Zeros of a Polynomial Function 1. Given the function: f (x) = x3 – x2 – 2x a.) Find all the real zeros. b.) Sketch the graph of the function by hand (using knowledge about end behaviors, zeros, y-intercept, and additional points in-between zeros).

2.2: Finding Zeros of a Polynomial Function 2. Given the function: f (x) = 3x4 – 4x3 a.) Find all the real zeros. b.) Sketch the graph of the function by hand (using knowledge about end behaviors, zeros, y-intercept, and additional points in-between zeros).

2.2: Finding Zeros of a Polynomial Function 3. Given the function: f (x) = -2x3 + 6x2 – 9/2x a.) Find all the real zeros. b.) Sketch the graph of the function by hand (using knowledge about end behaviors, zeros, y-intercept, and additional points in-between zeros).

2.2: Finding Zeros of a Polynomial Function Find a polynomial function that has the given zeros. 1.) 0, -2, -3 2.)

2.2: Finding Zeros of a Polynomial Function Find a polynomial function that has the given zeros. 3.) zero: -4, multiplicity: 2 zero: 3, multiplicity: 2

HW tomorrow: 2.3: p.126 (88-98 even) Pre-Calculus Honors Zeros of a function HW tomorrow: 2.3: p.126 (88-98 even) HW assignment #2: 2.3: p.127 (105-108 all) Copyright © Cengage Learning. All rights reserved.

2.3: Finding Real Zeros of a Polynomial Function 1. Find the real zeros of

2.3: Finding Real Zeros of a Polynomial Function 2. Find the real zeros of

2.2, 2.3: Zeros recap. What are the methods for finding zeros of a polynomial function?

2.3: Finding Real Zeros of a Polynomial Function 3. Find the real zeros of

2.3: Finding Real Zeros of a Polynomial Function 4. Find the real zeros of

2.3: Finding Real Zeros of a Polynomial Function 5. Find the real zeros of