Polynomial Functions of Higher Degree

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• Polynomial Functions of Higher Degree

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Quick Review

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Quick Review Solutions

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What youll learn about

• How to use transformations to sketch graphs of
  Polynomial Functions
• How to use the Leading Coefficient Test to
  determine End Behavior of Polynomial Functions
• How to find and use Zeros of Polynomial Functions
• How to use the Intermediate Value Theorem to
  locate zeros
• and why
• These topics are important in modeling various
  aspects of nature and can be used to provide
  approximations to more complicated functions.

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Example Graphing Transformations of Monomial
Functions

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Example Graphing Transformations of Monomial
Functions

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Cubic Functions
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Quartic Function
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Local Extrema and Zeros of Polynomial Functions

• A polynomial function of degree n has at most n
  1 local extrema and at most n zeros.

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Example Applying Polynomial Theory

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Example Applying Polynomial Theory

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Example Finding the Zeros of a Polynomial Function

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Example Finding the Zeros of a Polynomial Function

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Example Sketching the Graph of a Factored
Polynomial

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Example Sketching the Graph of a Factored
Polynomial

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Intermediate Value Theorem

• If a and b are real numbers with a lt b and if f
  is continuous on the interval a,b, then f takes
  on every value between f(a) and f(b). In other
• words, if y0 is between f(a) and f(b), then
  y0f(c) for some number c in a,b.