Quadratic Model for Car Mileage

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, 21.3 45, 31.9 15, 23.7 50, 29.5 20, 25.9 55, 27.6 25, 27.6 60, 25.3 30, 29.4 65, 23.0 35, 31.0 70, 20.0 40, 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, 21.3 45, 31.9 15, 23.7 50, 29.5 20, 25.9 55, 27.6 25, 27.6 60, 25.3 30, 29.4 65, 23.0 35, 31.0 70, 20.0 40, 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.

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

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

12. x-intercepts (2,0) and

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

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

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.

21. #9 Divide by x - 3 using long division.

22. x - 3

23. #10 Divide by

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

31. #14 Find the real zeros of

33. #15 List all possible rational zeros of the function

35. #16 Write as a product of linear factors.

37. #17 Write in standard form.

39. #18 Write in standard form.

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.

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

49. #23 Find all the asymptotes of