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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, 21.345, 31.9 15, 23.750, 29.5 20, 25.955, 27.6 25, 27.660, 25.3 30, 29.465, 23.0 35, 31.070, 20.0 40, 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, 21.345, 31.9 15, 23.750, 29.5 20, 25.955, 27.6 25, 27.660, 25.3 30, 29.465, 23.0 35, 31.070, 20.0 40, 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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Polynomial and Rational Functions. Sketch and analyze graphs of quadratic and polynomial functions. Use long division and synthetic division to.

Polynomial and Rational Functions. Sketch and analyze graphs of quadratic and polynomial functions. Use long division and synthetic division to.

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