1. Find the roots of f(x) = x2 – 5x + 6. A.1 and 5 B. –2 and –3C. 2 and 3 D. There are no roots.

2. Find the solutions of 6m2 – m = 12. A. and B. and

C. and D. There are no solutions.

3. What are the zeroes of f(x) = 4x2 + 4x – 35 A. and B. and

C. and D. There are no zeroes.

3

2

4

3

3

2

4

3

2

3

3

4

5

2

7

2

5

2

7

2

5

2

7

2

4. Which graph represents a function whose corresponding quadratic equation has no solutions?

A. B.

C. D.

5. Which graph represents a function whose corresponding quadratic equation has exactly one solutions?

A. B.

C. D.

6. Which graph represents a function whose corresponding quadratic equation has two solutions?

A. B.

C. D.

7. What are the root(s) of the quadratic equation whose related function is graphed? A. –1 and –3B. –1 and 4C. 4D. 1 and –3

8. What is the maximum value of the quadratic equation whose related function is graphed? A. –1 and –3B. –1 and 4C. 4D. 1 and –3

9. What is the vertex of the quadratic equation whose related function is graphed? A. (4, –1)B. (–1, 4)C. (0, 4)D. (4, 0)

10. What is the axis of symmetry of the quadratic equation whose related function is graphed? A. x = –1B. x = 4C. y = –1D. y = 4 

11. Find the vertex of the parabola whose graph is represented by y = –2x2 + 3x + 14. A. (0.75, 0) B. (–0.75, 10.625) C. (–0.75, 0) D. (0.75, 15.125)

12. What is the axis of symmetry of the parabola whose graph is represented by y = x2 + 3x – 10? A. y = B. x = C. x = D. y =

13. What is the minimum value of y = 2x2 – 4x + 8? A. 8 B. 2 C. 4 D. 6

13

4

3

2

3

2

49

4

14. What is(are) the x-intercept(s) of y = 3x2 + 6x – 45? A. 3 and –5 B. 5 and –3 C. –45 D. (–1, –48)  15. What is(are) the y-intercept(s) of y = x2 + 4x + 2? A. 2 and –2 B. –2 C. 2 D. (–2, –2)  16. The curve y = –2x2 – 6x – 4  A. has a maximum because the coefficient of the squared term is negative.B. has a minimum because the coefficient of the squared term is negative.C. has a maximum because the coefficient of the x term is negative.D. has a minimum because the coefficient of the x term is negative.

17. What is the range of the function f(x) = –4x2 + 3? A. all real numbers less than or equal to 3B. all real numbers greater than or equal to 3C. all integers less than or equal to 3D. all integers greater than or equal to 3  18. Which best describes the solution(s) of x2 – 2x + 2 = 0? A. no real solutionsB. 2 positive solutionsC. 1 positive and 1 negative solutionD. 2 negative solutions

19. For which values of x is f(x) = 2x2 – 12x + 23 increasing? A. x < 3 B. x > 3 C. 3 < x < 5 D. x > 23   20. For which values of x is f(x) = 2x2 – 12x + 23 decreasing? A.x < 3 B. x > 3 C. 3 < x < 5 D. x > 23

21. For which values of x is f(x) = –x2 + 6x + 7 positive? A.x < –1 or x > 7 B. –1 < x < 7C. –7 < x < 1 D. x < –7 or x > 1

22. For which values of x is f(x) = –x2 + 6x + 7 negative? A.x < –1 or x > 7 B. –1 < x < 7C. –7 < x < 1 D. x < –7 or x > 1 23. What are the solutions for x2 +5 = 29? A. ±72 B. ±36 C. ± D. ±   24. What is the solution set for the equation (x – 3)2 = 49? A. { } B. {± } C. {–4, 10} D. {–4, –10}

2 6 6 2

2 10 2 10

25. For which function(s) is the vertex at the maximum point? I. y = 6 + 3x – 4x2 II. y = 2(x – 7)2 + 5 III. y = –(x + 5)(x – 4) IV. y = 3x2 – 18x + 27 A. I only B. II and IV C. I and III D. I and IV  

26. For which function(s) is the vertex at the minimum point? I. y = 6 + 3x – 4x2 II. y = 2(x – 7)2 + 5 III. y = –(x + 5)(x – 4) IV. y = 3x2 – 18x + 27 A. I only B. II and IV C. I and III D. I and IV

27. For which function(s) will there be 2 real roots? I. y = 6 + 3x – 4x2 II. y = 2(x – 7)2 + 5 III. y = –(x + 5)(x – 4) IV. y = 3x2 – 18x + 27 A. III only B. II only C. I and III D. IV only   28. For which function(s) will there be no real roots? I. y = 6 + 3x – 4x2 II. y = 2(x – 7)2 + 5 III. y = –(x + 5)(x – 4) IV. y = 3x2 – 18x + 27 A. III only B. II only C. I and III D. IV only

29. For which function(s) will there be exactly one real root? I. y = 6 + 3x – 4x2 II. y = 2(x – 7)2 + 5 III. y = –(x + 5)(x – 4) IV. y = 3x2 – 18x + 27 A. III only B. II only C. I and III D. IV only 30. If a function f(x) is quadratic, with the characteristics shown below, which is the solution set of f(x) = 0? vertex: (1, –9) y-intercept: –8 x-intercepts: –2, 4 A. {2, –4} B. {–2, 4} C. {1, –9} D. {–8} 31. If a function f(x) is quadratic, with the characteristics shown below, which is the maximum or minimum value of the function? vertex: (1, –9) y-intercept: –8 x-intercepts: –2, 4 A. 1 B. –9 C. –8 D. –2, 4

32. From the top of a 200-foot tall building, a flare is launched straight up with an initial velocity of 64 feet per second. The height h after t seconds is given by h = –16t2 + 64t + 200. How many seconds does it take for the flare to reach its maximum height? A. 2 seconds B. 6 seconds C. 3 seconds D. 4 seconds   33. From the top of a 200-foot tall building, a flare is launched straight up with an initial velocity of 64 feet per second. The height h after t seconds is given by h = –16t2 + 64t + 200. How many seconds does it take for the flare to be even with the top of the building? A. 2 seconds B. 6 seconds C. 3 seconds D. 4 seconds 

34. From the top of a 200-foot tall building, a flare is launched straight up with an initial velocity of 64 feet per second. The height h after t seconds is given by h = –16t2 + 64t + 200. To the nearest second, how many seconds does it take for the flare to hit the ground? A. 2 seconds B. 6 seconds C. 3 seconds D. 4 seconds   35. Sam is fencing in a dog pen along a wall of his house. He has 80 feet of fencing. What is the value of x that would provide the greatest possible area? A. 26.667 feet B. 40 feetC. 20 feet D. 15.5 feet

x x

House

 36. Sam is fencing in a dog pen along a wall of his house. He has 80 feet of fencing. What is the greatest possible area? A. 400 feet2 B. 240.25 feet2

C. 1600 feet2 D. 800 feet2

   

37. Last year, the SportsTime Athletic Club charged $20 to participate in an aerobics class. Seventy people attended the classes. The club wants to increase the class price this year. They expect to lose one customer for each $1 increase in the price. How much should the club increase the charge to maximize the income from the aerobics classes? A. $25 B. $45 C. $55 D. $70

 

x x

House

38. Last year, the SportsTime Athletic Club charged $20 to participate in an aerobics class. Seventy people attended the classes. The club wants to increase the class price this year. They expect to lose one customer for each $1 increase in the price. What price should the club charge to maximize the income from the aerobics classes? A. $25 B. $45 C. $55 D. $70

39. Last year, the SportsTime Athletic Club charged $20 to participate in an aerobics class. Seventy people attended the classes. The club wants to increase the class price this year. What is the maximum income the SportsTime Athletic Club can expect to make? A. $2025 B. $625 C. $4900 D. $3025 

40. Last year, the SportsTime Athletic Club charged $20 to participate in an aerobics class. Seventy people attended the classes. The club wants to increase the class price this year. They expect to lose one customer for each $1 increase in the price. What increase would result in the club making no profit?

A.$25 B. $45 C. $55 D. $70

41. Paul uses the function y = –9x2 + 90x – 189 to model the profits made from selling cookies, where y is the profit in dollars and x is the month (x = 1 represents January). Which months is a profit predicted? A. January, February, March B. March. April, MayC. October, November, December D. April, May, June

42. Paul uses the function y = –9x2 + 90x – 189 to model the profits made from selling cookies, where y is the profit in dollars and x is the month (x = 1 represents January). Which months is 0 profit predicted? A. February, November B. March. JulyC. April, December D. May, October  43. Paul uses the function y = –9x2 + 90x – 189 to model the profits made from selling cookies, where y is the profit in dollars and x is the month (x = 1 represents January). Which month is the maximum profit predicted? A. August B. JuneC. December D. May

44. Paul uses the function y = –9x2 + 90x – 189 to model the profits made from selling cookies, where y is the profit in dollars and x is the month (x = 1 represents January). What is the maximum profit predicted? A. $27 B. $414C. $36 D. $270  45. Rodeo Rodney wants to fence in his horses in a rectangular region. He has a 500-foot roll of fencing and a large field. What is the length of the rectangle that would maximize the area?  A. 50 feet B. 125 feet C. 25 feet D. 250 feet

46. Rodeo Rodney wants to fence in his horses in a rectangular region. He has a 500-foot roll of fencing and a large field. What is the maximum area of the fenced in region?  A. 625 square feet B. 62,500 square feetC. 15,625 square feet D. 2500 square feet   47. You have a 1200-foot roll of fencing. You want to make two paddocks by splitting a rectangular enclosure in half. What is the width of the enclosure with the largest area?  A. 300 feet B. 120 feetC. 400 feetD. 200 feet

48. You have a 1200-foot roll of fencing. You want to make two paddocks by splitting a rectangular enclosure in half. What is the maximum area of the enclosure?  A. 80,000 square feet B. 90,000 square feetC. 60,000 square feetD. 14,400 square feet

49.Your factory produces lemon-scented widgets. You know that if each unit is cheaper, the more you can produce. But you also know that costs will eventually go up if you make too many widgets, due to the cost of storage of the overstock. The accountant says that your cost, C, in dollars for producing x thousands of units a day can be approximated by the formula C = 0.04x2 – 8.504x + 25302. Find the daily production level that will minimize your costs. A. 106.3 units B. 1063 units C. 10,630 units D. 106,300 units

50. Your factory produces lemon-scented widgets. You know that if each unit is cheaper, the more you can produce. But you also know that costs will eventually go up if you make too many widgets, due to the cost of storage of the overstock. The accountant says that your cost, C, in dollars for producing x thousands of units a day can be approximated by the formula C = 0.04x2 – 8.504x + 25302. Find the minimum cost for producing your widgets. A. $237,381 B. $24,850 B. C. $61,461 D. $4,454,780

51. George runs a canoe-rental business on the Tar River. He currently charges $12 per canoe and averages 36 rentals a day. An industry journal says that, for very fifty-cent increase in rental price, the average business can expect to lose two rentals per day. What should George charge to maximize his income?

A. $15 B. $13.50 C. $10.50 D. $9  52. George runs a canoe-rental business on the Tar River. He currently charges $12 per canoe and averages 36 rentals a day. An industry journal says that, for very fifty-cent increase in rental price, the average business can expect to lose two rentals per day. What is the maximum income per day?  A. $441 B. $405 C. $495 D. $351

53. A local grocery store has plans to construct a rectangular parking lot on land that is bordered on one side by a highway. There are 1280 feet of fencing available to enclose the other 3 sides. Let x represent the length of the two parallel sides of fencing. Find the dimensions that will maximize the area of the parking lot. A.480 ft. by 160 ft. B. 640 ft. by 320 ft.B.C. 320 ft. by 320 ft. D. 960 ft. by 160 ft. 

54. A local grocery store has plans to construct a rectangular parking lot on land that is bordered on one side by a highway. There are 1280 feet of fencing available to enclose the other 3 sides. Let x represent the length of the two parallel sides of fencing. Find the maximum area of the parking lot. A.204,800 square feet B. 76,800 square ft.B.C. 921,600 square ft. D. 102,400 square ft.

55. The height h (in feet) of a baseball t seconds after being hit is given by h(t) = –16t2 + 80t + 3. How many seconds will it take the baseball to reach its maximum height? A. 2 seconds B. 2.5 seconds C. 3 seconds D. 3.5 seconds 56. The height h (in feet) of a baseball t seconds after being hit is given by h(t) = –16t2 + 80t + 3. What is the maximum height of the baseball? A. 3 feet B. 99 feet C. 103 feet D. 125 feet 

57. The height h (in feet) of a baseball t seconds after being hit is given by h(t) = –16t2 + 80t + 3. What is the height of the baseball upon impact with the bat? A. 3 feet B. 99 feet C. 103 feet D. 125 feet

58. From 4 feet above a swimming pool, Susan throws a volleyball upward with a velocity of 32 feet per second. The height h(t) of the ball t seconds after Susan throws it is given by h(t) = –16t2 + 32t + 4. How many seconds will it take the volleyball to reach its maximum height? A.1 seconds B. 1.5 seconds C. 2 seconds D. 2.5 seconds

59. From 4 feet above a swimming pool, Susan throws a volleyball upward with a velocity of 32 feet per second. The height h(t) of the ball t seconds after Susan throws it is given by h(t) = –16t2 + 32t + 4. What is the maximum height of the baseball? A. 52 feet B. 100 feet C. 20 feet D. 4 feet

60. From 4 feet above a swimming pool, Susan throws a volleyball upward with a velocity of 32 feet per second. The height h(t) of the ball t seconds after Susan throws it is given by h(t) = –16t2 + 32t + 4. How many seconds will it take the ball to be level with Susan? A.1 seconds B. 1.5 seconds C. 2 seconds D. 2.5 seconds

61. From 4 feet above a swimming pool, Susan throws a volleyball upward with a velocity of 32 feet per second. The height h(t) of the ball t seconds after Susan throws it is given by h(t) = –16t2 + 32t + 4. To the nearest hundredth, how many seconds will it take the ball to hit the water? A.1.36 seconds B. 2.11 seconds C. 2.64 seconds D. 3.27 seconds

62. There is a hostile alien UFO hovering over Greenville at an altitude of 9,600 feet. Greenville Police plans to shoot it down. The weapon they will use is capable of firing with an initial velocity of 980 feet per second. The height of the bullet t seconds after firing is found by the function h(t) = –16t2 + 992t. What is the maximum height of the bullet’s trajectory? Is it possible for the bullet to hit the UFO? A.15,376 feet, No B. 8,320 feet, Yes C. 8,320 feet, No D. 15,376 feet, Yes

63. There is a hostile alien UFO hovering over Greenville at an altitude of 9,600 feet. Greenville Police plans to shoot it down. The weapon they will use is capable of firing with an initial velocity of 980 feet per second. The height of the bullet t seconds after firing is found by the function h(t) = –16t2 + 992t. How many seconds will it take for the bullet to reach its maximum height? A. 12 seconds B. 31 seconds C. 62 seconds D. 47 seconds

64. There is a hostile alien UFO hovering over Greenville at an altitude of 9,600 feet. Greenville Police plans to shoot it down. The weapon they will use is capable of firing with an initial velocity of 980 feet per second. The height of the bullet t seconds after firing is found by the function h(t) = –16t2 + 992t. How many seconds will it take for the bullet to hit its target?

A. 12 seconds B. 31 seconds C. 62 seconds D. 47 seconds

65. There is a hostile alien UFO hovering over Greenville at an altitude of 9,600 feet. Greenville Police plans to shoot it down. The weapon they will use is capable of firing with an initial velocity of 980 feet per second. The height of the bullet t seconds after firing is found by the function h(t) = –16t2 + 992t. If Deputy Dead-eye can’t aim correctly and misses the UFO, how many seconds will it take for the bullet to hit the ground? A. 12 seconds B. 31 seconds C. 62 seconds D. 47 seconds