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Polynomial function:

Polynomial functions are of the form where are constants, and is a positive integer The degree of a polynomial is , which is the highest power of in the function. They can be categorized into two types: odd power function and even power function. For your activity,
  • Use the sliders to change the values of the coefficients and observe how the graph changes.
  • Observe the zeros (x-intercepts), and the end behavior of the graph.
  • Answer the guiding questions that follow.

Example of even power polynomial function:

Quadratic function,

QUESTIONS:

  • What do you notice about the end behavior of the graph when the leading coefficient is positive? Negative?
  • How many x-intercepts (zeros) can the graph have at most?
  • What generalizations can you make about the graphs of even-degree polynomials?
  • Example of Odd Power Polynomial Function:

    Cubic function,
  • QUESTIONS:

  • What do you observe about the end behavior of the graph when the leading coefficient is positive? Negative?
  • How many x-intercepts (zeros) can the graph have at most?
  • What generalizations can you make about the graphs of odd-degree polynomials?