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Published byCameron Walton Modified over 6 years ago

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**Today in Pre-Calculus Go over homework Notes: (need calculator & book)**

Graphs of Polynomial Functions End Behavior Zeros Homework

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**End Behavior of Polynomial Functions**

Page 203 Exploration 1 If degree of polynomial is odd If degree of polynomial is even If leading coefficient is negative: graph reflects over x-axis so the end behavior changes signs.

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**End Behavior of Polynomial Functions**

Examples: Describe the end behavior of the following functions without graphing them. 1) f(x) = x3 + 2x2 – 11x – 12 2) g(x) =–2x4 + 2x3 – 22x2 – 18x + 35

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**Finding Zeros of Polynomial Functions**

Example: Find the zeros of f(x) = 5x3 – 5x2 – 30x 5x3 – 5x2 – 30x = 0 set equal to zero 5x(x2 – x – 6) = 0 factor GCF 5x(x – 3)(x + 2) = 0 factor 5x = 0 x – 3 = 0 x + 2 = 0 set EVERY term = 0 x = 0, 3, solve for x

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Multiplicity of a Zero If f is a polynomial function and (x – c)m is a factor of f, then c is a zero of multiplicity m. (c is a repeated zero). Example: f(x) = (x – 2)3(x+1)2 If the multiplicity is odd, then the graph crosses the x-axis at (c,0) and the value of f changes sign at x = c If the multiplicity is even, then the graph touches (but does not cross) the x-axis at (c,0) and the value of f does NOT change sign at x = c

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**Homework Pg. 209: 9-12, 26-28, 34, 36, 39-41 Bring books tomorrow**

Quiz: Friday, October 24

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