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.
Vocabulary
- degree of a polynomial
- end behavior
- multiple zeros
- multiplicity
About the Lesson
In this lesson, students utilize graphs and equations of five polynomial functions to determine the zeros of these five functions and whether the functions cross the x-axis 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.