# title of lesson: polynomial functions of higher degrees

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Title of Lesson

Title of Lesson: Polynomial Functions of Higher Degrees

By the end of this lesson, I will be able to answer the following questions1. How do I sketch graphs of polynomial functions using intercepts, end behavior and strategic points?

2. How do I build functions using intercepts and clues?

3. How do I Build polynomials functions given a real-world scenario and analyze the results using a graphing calc.

4. What is the Intermediate Value Theorem and what is it used for?

Vocabulary1. Multiplicity: Repeated zeros of a function

2. Intermediate Value Theorem: Let a and b be real numbers such that a < b and there is some value c which is on the interval [a,b] that guarantees

Prerequisite Skills with PracticeCalculator discovery:Monomials of higher degrees(use different colors)

Properties ofPolynomial graphs

They are always Continuous, that is they have no breaks

They are smooth and rounded no sharp turns

They have predicable endbehavior.

Leading Coefficient Test

End Behavior

Leading Coefficient Test

Using the Leading Coefficient Test.

Describe the end behavior of the following functions

Finding zeros of a polynomial function.

Introducing multiplicities.

Making sketches based on end behavior and intercepts

Find a polynomial with integer coefficients given the following zeros.

Using the Intermediate Value Theorem to prove existence of zeros.

Find three intervals of length 1 in which the polynomial below is guaranteed to have a zero.

A rancher has 374 feet of fencing to enclose twoadjacent rectangular corrals.

Write a function for the total area with respect to x.

2. Use a graphing calculator to approximate the dimensions that will produce the maximumArea.Homework:

Page 112: 9,10 (15-43) odd (45-48) all (49-63) odd (79-82) all 91,92 (105-107) all

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