3-7 investigating graphs of polynomial functions- …edweb.tusd1.org/jdumes/documents/algebra...
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37 Investigating Graphs of Polynomial Functions period 1.notebook
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Bellwork 11-3-14
Identify all the real roots of each equation.
1. x3 – 7x2 + 8x + 16 = 0 2. 2x3 – 14x – 12 = 0
37 Investigating Graphs of Polynomial Functions period 1.notebook
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Use properties of end behavior to analyze, describe, and graph polynomial functions.
Identify and use maxima and minima of polynomial functions to solve problems.
Objectives
37 Investigating Graphs of Polynomial Functions period 1.notebook
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end behaviorturning pointlocal maximumlocal minimum
Vocabulary
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Polynomial functions are classified by their degree. The graphs of polynomial functions are classified by the degree of the polynomial. Each graph, based on the degree, has a distinctive shape and characteristics.
37 Investigating Graphs of Polynomial Functions period 1.notebook
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End behavior is a description of the values of the function as x approaches infinity or negative infinity . The degree and leading coefficient of a polynomial function determine its end behavior. It is helpful when you are graphing a polynomial function to know about the end behavior of the function.
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37 Investigating Graphs of Polynomial Functions period 1.notebook
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Identify the leading coefficient, degree, and end behavior.
Example 1: Determining End Behavior of Polynomial Functions
A. Q(x) = –x4 + 6x3 – x + 9 B. P(x) = 2x5 + 6x4 – x + 4
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Check It Out! Example 1 Identify the leading coefficient, degree, and end behavior.
a. P(x) = 2x5 + 3x2 – 4x – 1 b. S(x) = –3x2 + x + 1
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Example 2A: Using Graphs to Analyze Polynomial Functions
Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
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Example 2B: Using Graphs to Analyze Polynomial Functions
Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
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Check It Out! Example 2a Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
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Check It Out! Example 2b Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
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Homework: Practice A Worksheet 3-7, #'s 1-10 all