Education Technology

Multiplicity of Zeros of Functions

Updated on 06/12/2015

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.