1. Polynomial Functions of Higher Degree
Objective: Students will be able to identify properties of higher degree polynomials and sketch graphs using these properties.

2. Polynomial Vocab
A polynomial is made up of monomials or terms

3. Basic Transformations
Remember from unit 1 how a graph moves right or left, up or down, narrow and wide, flip

4. Local Extremes and Zeros
A polynomial function of degree n has at most n-1 local extremes (min or max) and at most n zeros
Degree 2
Has 1 min
Has 2 zeros

5. End Behavior
Pg 203 in book
End behavior is associated with the degree of the polynomial and the leading coefficient.
What are the rules you could come up with?

6. Example
Describe the end behavior of the following polynomials, use words and in terms of limits

7. Zeros and Polynomials
Factor Set each factor equal to zero and solve for x

8. Repeated zeros
If polynomial is (x-c)^m then c is a repeated zero for the polynomial (x-2)^2 gives you (x-2)(x-2) both give you 2 This is also known as the multiplicity of the zero If exponent is even then the graph touches that point but does not cross If the exponent is odd it crosses at that point

9. Example

10. Intermediate Value Theorem
This helps us to determine if the graph would cross the axis at the points are just touch that point

11. Homework
Pg 209 8,9-12,29-32, 34, 39,41,