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Example 2 The following table gives the mileage y, in miles per gallon, of a certain car at various speeds x (in miles per hour). a) Use a graphing utility.

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Presentation on theme: "Example 2 The following table gives the mileage y, in miles per gallon, of a certain car at various speeds x (in miles per hour). a) Use a graphing utility."— Presentation transcript:

1 Example 2 The following table gives the mileage y, in miles per gallon, of a certain car at various speeds x (in miles per hour). a) Use a graphing utility to create a scatter plot of the data. b) Use the regression feature of a graphing utility to find a quadratic model that best fits the data. c) Use the model to predict the speed that gives the greatest mileage. Speed, x Mileage, y 10, , , , , , , , , , , , , 31.7

2 Example 2 The following table gives the mileage y, in miles per gallon, of a certain car at various speeds x (in miles per hour). a) Use a graphing utility to create a scatter plot of the data. b) Use the regression feature of a graphing utility to find a quadratic model that best fits the data. c) Use the model to predict the speed that gives the greatest mileage. Speed, x Mileage, y 10, , , , , , , , , , , , , 31.7

3 Example 3 For the data points below, determine whether a linear model or a quadratic model best fits the data. (1, 5) (2, 6) (3, 8) (4, 9) (5, 11) (6, 10) (7, 11) (8, 12) (9, 14) (10, 16)

4 Example 3 For the data points below, determine whether a linear model or a quadratic model best fits the data. (1, 5) (2, 6) (3, 8) (4, 9) (5, 11) (6, 10) (7, 11) (8, 12) (9, 14) (10, 16)

5 #1 Sketch the graph of by hand and identify the vertex and the intercepts.

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7 #2 Find the number of units that produce a minimum cost C if

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9 #3 Find the quadratic function that has a maximum at (1, 7) and passes through the point (2, 5).

10 maximum at (1, 7) and passes through the point (2, 5).

11 #4 Find two quadratic functions that have x-intercepts (2,0) and

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13 #5 Use the leading Coefficient Test to determine the right-hand and left-hand behavior of the graph of the polynomial function

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15 #6 Find all the real zeros of Verify your answer with a graphing utility.

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17 #7 Find a polynomial function with 0, 3, and -2 as zeros.

18 0, 3, and -2 as zeros.

19 #8 Sketch by hand.

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21 #9 Divideby x - 3 using long division.

22 x - 3

23 #10 Divide by

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25 #11 Use synthetic division to divide by x + 5.

26 x + 5

27 #12 Use synthetic division to find f(-6) when

28 f(-6)

29 #13 Find the real zeros of

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31 #14 Find the real zeros of

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33 #15 List all possible rational zeros of the function

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35 #16 Write as a product of linear factors.

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37 #17 Write in standard form.

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39 #18 Writein standard form.

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41 #19 Find a polynomial with real coefficients that has 2, 3 + i, and 3 - 2i as zeros.

42 2, 3 + i, and 3 - 2i as zeros

43 #20 Use synthetic division to show that 3i is a zero of

44 3i

45 #21 Sketch the graph of and label all intercepts and asymptotes.

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47 #22 Sketch the graph of and label all intercepts and asymptotes.

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49 #23 Find all the asymptotes of

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51 #24 Find all the asymptotes of

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53 #25 Sketch the graph of

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55

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