See Problem 2.

Use the quadratic formula to solve each equation. Round your answer to the nearest hundredth.

16. x 2 + 8 x + 11 = 0 x squared , plus 8 . x plus 11 equals 0
17. 5 x 2 + 12 x − 2 = 0 5 x squared , plus 12 x minus 2 equals 0
18. 2 x 2 − 16 x = − 25 2 x squared , minus 16 x equals negative 25
19. 8 x 2 − 7 x − 5 = 0 8 x squared , minus 7 x minus 5 equals 0
20. 6 x 2 + 9 x = 32 6 x squared , plus 9 x equals 32
21. 3 x 2 + 5 x = 4 3 x squared , plus 5 x equals 4
22. Football A football player punts a ball. The path of the ball can be modeled by the equation y = − 0.004 x 2 + x + 2.5 , y equals negative . 0.004 , x squared . plus x plus 2.5 comma  where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball. How far from the football player will the ball land? Round to the nearest tenth of a foot.

See Problem 3.

Which method(s) would you choose to solve each equation? Justify your reasoning.

23. x 2 + 4 x − 15 = 0 x squared , plus 4 . x minus 15 equals 0
24. 9 x 2 − 49 = 0 9 x squared , minus 49 equals 0
25. 4 x 2 − 41 x = 73 4 x squared , minus 41 x equals 73
26. 3 x 2 − 7 x + 3 = 0 3 x squared , minus 7 x plus 3 equals 0
27. x 2 + 4 x − 60 = 0 x squared , plus 4 . x minus 60 equals 0
28. − 4 x 2 + 8 x + 1 = 0 negative 4 x squared . plus 8 x plus 1 equals 0

See Problem 4.

Find the number of real-number solutions of each equation.

29. x 2 − 2 x + 3 = 0 x squared , minus 2 . x plus 3 equals 0
30. x 2 + 7 x − 5 = 0 x squared , plus 7 . x minus 5 equals 0
31. x 2 + 3 x + 11 = 0 x squared , plus 3 . x plus 11 equals 0
32. x 2 − 15 = 0 x squared , minus 15 equals 0
33. x 2 + 2 x = 0 x squared , plus 2 . x equals 0
34. 9 x 2 + 12 x + 4 = 0 9 x squared , plus 12 x plus 4 equals 0

B Apply

Use any method to solve each equation. If necessary, round your answer to the nearest hundredth.

35. 3 w 2 = 48 3 w squared , equals 48
36. 3 x 2 + 2 x − 4 = 0 3 x squared , plus 2 x minus 4 equals 0
37. 6 g 2 − 18 = 0 6 g squared , minus 18 equals 0
38. 3 p 2 + 4 p = 10 3 p squared , plus 4 p equals 10
39. k 2 − 4 k = − 4 k squared , minus 4 . k equals negative 4
40. 13 r 2 − 117 = 0 13 r squared , minus 117 equals 0

41. Think About a Plan You operate a dog-walking service. You have 50 customers per week when you charge $14 per walk. For each $1 decrease in your fee for walking a dog, you get 5 more customers per week. Can you ever earn $750 in a week? Explain.

    • What quadratic equation in standard form can you use to model this situation?
    • How can the discriminant of the equation help you solve the problem?

42. Sports Your school wants to take out an ad in the paper congratulating the basketball team on a successful season, as shown below. The area of the photo will be half the area of the entire ad. What is the value of x?

    

43. Writing How can you use the discriminant to write a quadratic equation that has two solutions?

44. Error Analysis Describe and correct the error below that a student made in finding the discriminant of 2 x 2 + 5 x − 6 = 0 . 2 x squared , plus 5 x minus 6 equals 0 .

    

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