Education Technology

Multiplicity of Zeros of Functions

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.