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Precalculus: Multiplicity of Zeros of Functions
by Texas Instruments

#### 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.