Algebra 2: Multiplicity of Zeros of Polynomial Functions
Multiplicity Exploration
Use the blue slider to change the power of (x + 2), the red slider to change the power of (x - 1), and the green slider to change the power of (x - 3). Once you are done exploring the applet, answer the 3 questions below the applet.
Question 1)
Describe how the graph behaves at a zero (x-intercept) when the multiplicity of that zero is an even number. Does it cross the x-axis or bounce off the x-axis? Explain how you know.
Question 2)
Describe how the graph behaves at a zero when the multiplicity of that zero is an odd number. Does it cross the x-axis or bounce off the x-axis? Explain how you know.
Question 3)
Describe how the graph behaves at a zero when the multiplicity of that zero increases. If the multiplicity of a zero was extremely large, what do you think the graph would look like at that zero? Explain how you know.