1. Title of Lesson: Polynomial Functions of Higher Degrees

2. 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?

3. 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

4. Prerequisite Skills with Practice Calculator discovery: Monomials of higher degrees… (use different colors)

5. Properties of Polynomial graphs They are always Continuous, that is – they have no breaks They are smooth and rounded – no sharp turns They have predicable end behavior.

6. Leading Coefficient Test End Behavior Leading Coefficient Test

7. Using the Leading Coefficient Test. Describe the end behavior of the following functions

9. Finding zeros of a polynomial function. Introducing multiplicities. Making sketches based on end behavior and intercepts

10. Find a polynomial with integer coefficients given the following zeros.

11. 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.

12. A rancher has 374 feet of fencing to enclose two adjacent 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 maximum Area.

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