# Multiplicity of zeros of functions student activity sheets

2.3 Polynomial Functions of Higher Degree with Modeling PreCalculus 2 - 7 Example 5: State the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding -xintercept. Using what you know about end behavior and the zeros ofthe

We say that x = h is a zero of multiplicity p. The graph of a polynomial function will touch the x -axis at zeros with even multiplicities. The graph will cross the x -axis at zeros with odd multiplicities. The sum of the multiplicities is the degree of the polynomial function. I plan to begin by having students complete page 2 of Multiplicity of Zeros Day 1 (p.1-2). If students do not recall zeros of a function, you can remind them. Here is a straight forward hint: find the values for x that make f (x) = 0. Push the students to come up with an algebraic solution,...

Use the slider to change the power of the factor (x+2) in the polynomial function. 1. What happens to the graph of the polynomial at the zero -2 as the multiplicity of the zero increases? 2. What happens to the graph of the polynomial at the zero -2 when the power of the factor (x+2) is even? 3 ...

In my discovery activity, my aim is for students to discover the pattern for determining the end behavior of higher degree polynomial functions. In the notes afterwards, my aim is to solidify this knowledge and to teach students how to sketch the graphs of these polynomials by finding their zeros. This lesson merges graphical and algebraic representations of a polynomial function and its linear factors. As a result, students will: Manipulate the parameters of the linear functions and observe the resulting changes in the polynomial function. Find the zeros of the polynomial equations by finding the zeros of the linear factors. one zero, it is still a quadratic function due to multiplicities of zeros. 7. Distribute copies of the attached Zeros and Factors handout, and have students complete it. 8. Have students do a matching activity, using the attached sets of Matching Cards, each set containing six cards that relate to each other. Either give small groups copies of all the