Title of Lesson: Polynomial Functions of Higher Degrees

By the end of this lesson, I will be able to answer the following questions…

1. 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?

Vocabulary

1. 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)

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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

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End Behavior

Leading Coefficient Test

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Using the Leading Coefficient Test.

Describe the end behavior of the following functions

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Finding zeros of a polynomial function.

Introducing multiplicities.

Making sketches based on end behavior and intercepts

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Find a polynomial with integer coefficients given the following zeros.

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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.

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

1. 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 •