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

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Presentation on theme: "Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.1 Polynomial Functions and Models."— Presentation transcript:

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

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

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5 Summary of the Properties of the Graphs of Polynomial Functions

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

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8 Figure 3

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

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11 Figure 6

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

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

17 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.

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

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23 Figure 16 (a)

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

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

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

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

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

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