Graphing a Fourth Degree Polynomial

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Taught by mrbrianmclogan
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Meets NCTM Standards:
Lesson Summary:

In this lesson, we learn how to graph a fourth degree polynomial without the use of a calculator. We use the leading coefficient test to determine the n-behavior of the graph, and then find the zeros by setting the polynomial equal to zero and factoring. We also use the intermediate value theorem to find additional points on the graph between the zeros. By using the multiplicity of each zero, we can determine if the graph will touch or cross the x-axis. Finally, we connect the points and use the n-behavior to complete the graph.

Lesson Description:

Graphing a fourth degree polynomial

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Questions answered by this video:
  • In g(x)=x⁴-4x² what is the multiplicity of 0?
  • What is the behaviour of the graph when the degree is even ?