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

Polynomial Vocab A polynomial is made up of monomials or terms

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

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

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?

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

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

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

Example

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

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