1. Find the roots of f(x) = x2

1

• 1. Find the roots of f(x) x2 5x 6.
•  
• 1 and 5 B. 2 and 3
• C. 2 and 3 D. There are no roots.
• 2. Find the solutions of 6m2 m 12.
•  
• and B. and
• and D. There are no solutions.
• 3. What are the zeroes of f(x) 4x2 4x 35
•  
• and B. and
• C. and D. There are no zeroes.

2
4. Which graph represents a function whose
corresponding quadratic equation has no
solutions? A. B.
C.
D.
3
5. Which graph represents a function whose
corresponding quadratic equation has exactly
one solutions? A. B.
C.
D.
4
6. Which graph represents a function whose
corresponding quadratic equation has two
solutions? A. B.
C.
D.
5
7. What are the root(s) of the quadratic equation
whose related function is graphed?   A. 1
and 3 B. 1 and 4 C. 4 D. 1 and 3
6
8. What is the maximum value of the quadratic
equation whose related function is graphed?   A.
1 and 3 B. 1 and 4 C. 4 D. 1 and 3
7
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)
8
10. What is the axis of symmetry of the quadratic
equation whose related function is graphed?   A.
x 1 B. x 4 C. y 1 D. y 4  
9

• Find the vertex of the parabola whose graph is
  represented by
• y 2x2 3x 14.
•  
• (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?
•  
• 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

10
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.
11
17. What is the range of the function f(x) 4x2
3?   A. all real numbers less than or equal to
3 B. all real numbers greater than or equal to
3 C. all integers less than or equal to 3 D. all
integers greater than or equal to 3     18. Which
best describes the solution(s) of x2 2x 2
0?   A. no real solutions B. 2 positive
solutions C. 1 positive and 1 negative
solution D. 2 negative solutions
12

• 19. For which values of x is f(x) 2x2 12x
  23 increasing?
•  
• A. x lt 3 B. x gt 3 C. 3 lt x lt 5 D. x gt 23
•  
•  
•  
• 20. For which values of x is f(x) 2x2 12x
  23 decreasing?
•  
• x lt 3 B. x gt 3 C. 3 lt x lt 5 D. x gt 23
• 21. For which values of x is f(x) x2 6x 7
  positive?
•  
• x lt 1 or x gt 7 B. 1 lt x lt 7
• C. 7 lt x lt 1 D. x lt 7 or x gt 1

13

• 22. For which values of x is f(x) x2 6x 7
  negative?
•  
• x lt 1 or x gt 7 B. 1 lt x lt 7
• C. 7 lt x lt 1 D. x lt 7 or x gt 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

14
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
15
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
16
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
17
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  
18
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
feet C. 20 feet D. 15.5 feet
19
 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  
20
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  
21

• 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?
• 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,
  May
• C. October, November, December D. April, May,
  June

22
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. July C.
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. June C. December D. May
23
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. 414 C. 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
24
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 feet C.
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
feet C. 400 feet D. 200 feet
25

• 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 feet
• C. 60,000 square feet
• D. 14,400 square feet
• 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

26

• 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.
•  
• 237,381 B. 24,850
• C. 61,461 D. 4,454,780

27
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
28

• 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.
•  
• 480 ft. by 160 ft. B. 640 ft. by 320 ft.
• 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.
•  
• 204,800 square feet B. 76,800 square ft.
• C. 921,600 square ft. D. 102,400 square ft.

29
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
30

• 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?
•  
• 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

31

• 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?
•  
• 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?
•  
• 1.36 seconds B. 2.11 seconds
• C. 2.64 seconds D. 3.27 seconds

32

• 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
• bullets trajectory? Is it possible for the
  bullet to hit the UFO?
•  
• 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

33
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 cant 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