#### Activity Overview

Students will utilize graphs and equations of five polynomial functions to determine the zeros of the functions and whether the functions cross the x-axis at these zeros or just touch the x-axis at the zeros. Then students will determine the degree of the polynomial functions and the effect the degree has upon the end behavior of the functions.

#### Objectives

- Students will determine the multiplicity of zeros of a polynomial function when given its graph or its equation in factored form.
- Students will write an equation for a polynomial function when given information about its zeros and the multiplicity of the zeros.
- Students will write an equation for a polynomial function when given its graph.
- Use appropriate tools strategically. (CCSS Mathematical Practice)
- Look for and make use of structure. (CCSS Mathematical Practice)

#### Vocabulary

This lesson involves students utilizing graphs and equations of five polynomial functions to determine the zeros of the functions and whether the functions cross the x-axis at these zeros or just touch the x-axis at the zeros.

As a result, students will:

- determine the degree of the polynomial functions and the effect the degree has upon the end behavior of the functions.
- write possible equations for a polynomial function when given information about its zeros.
- write the equations in factored form, given the graphs of three functions.

#### About the Lesson

This lesson involves students utilizing graphs and equations of five polynomial functions to determine the zeros of the functions and whether the functions cross the x-axis at these zeros or just touch the x-axis at the zeros.

As a result, students will:

- determine the degree of the polynomial functions and the effect the degree has upon the end behavior of the functions.
- write possible equations for a polynomial function when given information about its zeros.
- write the equations in factored form, given the graphs of three functions.