Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.1 Polynomial Functions and Models.

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Presentation transcript:

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.1 Polynomial Functions and Models

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Summary of the Properties of the Graphs of Polynomial Functions

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Figure 3

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Figure 6

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Find a polynomial of degree 3 whose zeros are -4, -2, and 3. Use a graphing utility to verify your result.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. For the polynomial, list all zeros and their multiplicities. 2 is a zero of multiplicity 1 because the exponent on the factor x – 2 is 1. –1 is a zero of multiplicity 3 because the exponent on the factor x + 1 is 3. 3 is a zero of multiplicity 4 because the exponent on the factor x – 3 is 4.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Figure 16 (a)

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Figure 16 (b)

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Figure 16 (d)

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The polynomial is degree 3 so the graph can turn at most 2 times.

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