This document discusses polynomial functions of higher degree and their modeling applications. It begins with vocabulary terms related to polynomials and explains how to classify polynomials based on their degree. It then covers identifying the end behavior of polynomials using the leading term test, and discusses how the sign of the leading coefficient affects the graphs of cubic and quartic functions. Examples are provided to demonstrate applying the leading term test. The document notes that polynomial functions can have at most n - 1 local extrema and n zeros, where n is the degree of the polynomial. It concludes by assigning homework on polynomials through MathXL.

1. Bell Ringer: Vocabulary
1. _________ is a function in which all
exponents are positive whole numbers.
2. _________ is a first degree polynomial
function.
3. _________is a second degree
polynomial function.
4. __________ is a polynomial function
with a degree of 0.
5. ________ is the highest exponent of a
polynomial.

2. Copyright © 2011 Pearson, Inc.
Polynomial
Functions of
Higher
Degree with
Modeling

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What you’ll learn about
 Graphs of Polynomial Functions
 End Behavior of Polynomial Functions
… and why
These topics are important in modeling and can be used
to provide approximations to more complicated
functions, as you will see if you study calculus.

4. Copyright © 2011 Pearson, Inc.
The Breakdown of a Polynomial

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Classifying Polynomials
Slide 2.3 - 5

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Practice
Slide 2.3 - 6

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Home Learning Preview
Slide 2.3 - 7

8. Copyright © 2011 Pearson, Inc.
Leading Term Test for
Polynomial End Behavior

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Leading Term Test
for Polynomial End Behavior


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Cubic Functions
If the Leading Coefficient
is positive
If the Leading Coefficient
is negative

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Quartic Function
If the Leading Coefficient
is positive
If the Leading Coefficient
is negative

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Leading Term Test for Polynomial End
Behavior

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Leading Term Test for Polynomial End
Behavior

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Example
Describe the end behavior of g(x)  2x4
 3x3
 x 1
using limits.

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Local Extrema and Zeros of
Polynomial Functions
A polynomial function of degree n has at most
n – 1 local extrema and at most n zeros.

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Match each graph with its proper function.
NO GRAPHING CALCULATOR!!!
Slide 2.3 - 18
1)
2)
3)
4)

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Home Learning Assignment
 “Introduction to Polynomials” on MathXL
 STUDY!!!
 Have a great safe weekend!