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.

• 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.

• degree of a polynomial
• end behavior
• multiple zeros
• multiplicity

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.

*Note: This activity contains an optional AP Practice Questions document for those students preparing for the AP Precalculus Exam.