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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 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

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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 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

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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)

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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)

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

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

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

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

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

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

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

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0, 3, and -2 as zeros.

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#8 Sketch by hand.

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#9 Divideby x - 3 using long division.

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x - 3

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#10 Divide by

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

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x + 5

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

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f(-6)

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#13 Find the real zeros of

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#14 Find the real zeros of

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#15 List all possible rational zeros of the function

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#16 Write as a product of linear factors.

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#17 Write in standard form.

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#18 Writein standard form.

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

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

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

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3i

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

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

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#23 Find all the asymptotes of

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#24 Find all the asymptotes of

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#25 Sketch the graph of

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