Multiplicity of a Zero

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Taught by mrbrianmclogan
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Meets NCTM Standards:
Lesson Summary:

This lesson discusses the concept of the multiplicity of a zero and how it affects the graph of a polynomial. A zero can have a repeated factor, which means the graph either crosses or touches the x-axis at that point, depending on the exponent. Understanding the multiplicity of zeros is crucial in finding the zeros and graphing any polynomial function. The lesson provides examples of how to graph polynomials with multiple zeros and varying multiplicities.

Lesson Description:

Overview of Multiplicity of a zero

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Questions answered by this video:
  • In the function f(x)=(x-a)^k what are the coordinates of the x-intercept?
  • In f(x)=(x-a)^k What is the behaviour of the graph when (i) k is odd (ii)k is even
  • what does it mean when a zero has a multiplicity?