# 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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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

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

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)

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)

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

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

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

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

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

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

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

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

0, 3, and -2 as zeros.

#8 Sketch by hand.

#9 Divideby x - 3 using long division.

x - 3

#10 Divide by

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

x + 5

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

f(-6)

#13 Find the real zeros of

#14 Find the real zeros of

#15 List all possible rational zeros of the function

#16 Write as a product of linear factors.

#17 Write in standard form.

#18 Writein standard form.

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

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

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

3i

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

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

#23 Find all the asymptotes of

#24 Find all the asymptotes of

#25 Sketch the graph of

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