Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
1.
|
Identify the vertex of the graph. Tell whether it is a minimum or
maximum.  a. | (0, –1); minimum | c. | (0, –1); maximum | b. | (–1, 0);
maximum | d. | (–1, 0);
minimum |
|
|
|
2.
|
Which of the quadratic functions has the narrowest graph?
|
|
|
3.
|
Which of the quadratic functions has the widest graph?
|
|
|
4.
|
Order the group of quadratic functions from widest to narrowest graph.  ,
 , 
|
|
|
5.
|
If  , then the graph of  is ________ narrower
than  . a. | always | b. | sometimes | c. | never |
|
|
|
6.
|
If an object is dropped from a height of 38 feet, the function  gives the
height of the object after t seconds. Graph the function.
|
|
|
7.
|
A parabola ________ has an axis of symmetry.
a. | always | b. | sometimes | c. | never |
|
|
|
8.
|
Find the equation of the axis of symmetry and the coordinates of the vertex of
the graph of the function. 
|
|
|
9.
|
Graph  . Label the axis of symmetry and vertex.
|
|
|
10.
|
Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The
function  , where x = width, gives you the area of the dog
pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the
nearest tenth as necessary. a. | width = 27 ft; area = 182.3 ft2 | c. | width = 13.5 ft; area = 546.8
ft2 | b. | width = 27 ft; area = 391.5 ft2 | d. | width = 13.5 ft; area = 182.3
ft2 |
|
|
|
11.
|
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height
h in feet after t seconds is given by the function  . a. In how many seconds does the ball reach its maximum height? Round
to the nearest hundredth if necessary.
b. What is the ball’s maximum
height? a. | 1.13 s; 69.75 ft | b. | 1.13 s; 29.25 ft | c. | 1.13 s; 31.5 ft | d. | 2.25 s; 9
ft |
|
|
|
12.
|
Graph  .
|
|
|
13.
|
Graph  .
|
|
|
14.
|
Graph  .
|
|
|
15.
|
Simplify  .
|
|
|
16.
|
Simplify  .
|
|
|
17.
|
The principal square root of a positive real number is ________ negative.
a. | always | b. | sometimes | c. | never |
|
|
|
18.
|
Simplify  . a. | –50 | b. |  | c. | 25 | d. | –25 |
|
|
|
19.
|
Is  rational or irrational?
|
|
|
20.
|
Is  rational or irrational?
|
|
|
21.
|
The expression  is ________ rational if a and b are
integers and  . a. | always | b. | sometimes | c. | never |
|
|
|
22.
|
Between what two consecutive integers is  ? a. | 11 and 12 | b. | 14 and 15 | c. | 12 and 13 | d. | 9 and
10 |
|
|
|
23.
|
The formula  gives the velocity v in feet per second of an
object that has fallen h feet. Find the velocity of an object that has fallen 76 feet. Round
to the nearest hundredth. a. | 12.33 ft/sec | b. | 69.74 ft/sec | c. | 4864 ft/sec | d. | 49.32
ft/sec |
|
|
|
24.
|
Solve  by graphing the related function. a. | 
There are two solutions: 2 and
–2. | c. | 
There are two solutions: 2 and
–2. | b. | 
There are two solutions:  . | d. | 
There are no real number solutions. |
|
|
|
25.
|
The quadratic equation  , where a > 0, ________ has
at least one real number solution. a. | always | b. | sometimes | c. | never |
|
|
|
Solve the equation using square roots.
|
|
|
26.
|
7  + 6 = 13 a. | no real number solutions | c. |  | b. | 1 | d. |  |
|
|
|
27.
|
a. |  | c. |  | b. | –4 | d. | no
real number solutions |
|
|
|
Solve the equation using the zero-product property.
|
|
|
28.
|
a. | x = –1 or x =  | c. | x = 1 or x =  | b. | x = –1 or x =  | d. | x = 1 or x =  |
|
|
|
29.
|
a. | n =  or n =  | c. | n = 0 or n =  | b. | n = 0 or n =  | d. | n =  or n =  |
|
|
|
30.
|
A sports recreation company plans to manufacture a beach ball with a surface
area of 7238 in. 2 Find the radius of the beach ball. Use the formula  , where
A is the surface area and r is the radius of the sphere. a. | 24 in. | b. | 48 in. | c. | 75 in. | d. | 576
in. |
|
|
|
31.
|
Find the value of x. If necessary, round to the nearest tenth.  a. | 7.3 in. | b. | 10.3 in. | c. | 12.4 in. | d. | 14.6
in. |
|
|
|
Solve the equation by factoring.
|
|
|
32.
|
a. | z = 3 or z = 9 | c. | z = –3 or z =
9 | b. | z = 3 or z = –9 | d. | z = –3 or z =
–9 |
|
|
|
33.
|
a. | z =  or z = –2 | c. | z = 3 or z =
–2 | b. | z =  or z = 2 | d. | z = 3 or z =
2 |
|
|
|
34.
|
a. | c = 0 or c = –4 | c. | c = 0 or c =
4 | b. | c = 0 or c =  | d. | c = 1 or c = – |
|
|
|
35.
|
|
|
|
36.
|
|
|
|
37.
|
The expression  ________ has the solution x = 0. a. | always | b. | sometimes | c. | never |
|
|
|
38.
|
Tasha is planning an expansion of a square flower garden in a city park. If each
side of the original garden is increased by 7 m, the new total area of the garden will be 144
m2. Find the length of each side of the original garden.
a. | 19 m | b. | 12 m | c. | 5 m | d. |  m |
|
|
|
39.
|
The area of a playground is 336 yd2. The width of the playground is 5
yd longer than its length. Find the length and width of the playground.
a. | length = 26 yd, width = 21 yd | c. | length = 21 yd, width = 16
yd | b. | length = 21 yd, width = 26 yd | d. | length = 16 yd, width = 21
yd |
|
|
|
40.
|
Solve the cubic equation by factoring. 
|
|
|
41.
|
Find the value of n such that  is a perfect square trinomial.
|
|
|
Solve the equation by completing the square. Round to the nearest hundredth
if necessary.
|
|
|
42.
|
a. | 5, –1 | b. | 11, –7 | c. | 1.73, –1.73 | d. | 1,
3 |
|
|
|
43.
|
a. | 4.66, 5.12 | b. | 3.62, –6.62 | c. | 3.55, –6.55 | d. | 24.75,
–27.75 |
|
|
|
44.
|
a. | 1.05, –4.05 | b. | 1.66, 2.69 | c. | 1.19, –4.19 | d. | –8.75,
5.75 |
|
|
|
45.
|
3  a. | 2.65, 3 | b. | –30, 36 | c. | 4, –2 | d. | 7.58,
–1.58 |
|
|
|
Use the quadratic formula to solve the equation. If necessary, round to the
nearest hundredth.
|
|
|
46.
|
a. | 18, 28 | b. | –9, –14 | c. | 9, 14 | d. | –18,
28 |
|
|
|
47.
|
a. | 1.82, –0.22 | b. | 11.2, –9.6 | c. | 3.64, –0.44 | d. | 0.22,
–1.82 |
|
|
|
48.
|
A rocket is launched from atop a 101-foot cliff with an initial velocity of 116
ft/s. a. Substitute the values into the vertical motion
formula  . Let h = 0. b. Use the quadratic
formula find out how long the rocket will take to hit the ground after it is launched. Round to the
nearest tenth of a second. a. |  ; 0.8 s | c. |  ; 0.8
s | b. |  ; 8 s | d. |  ; 8 s |
|
|
|
49.
|
The solutions given by the quadratic formula are ________ integers.
a. | sometimes | b. | always | c. | never |
|
|
|
Use any method to solve the equation. If necessary, round to the nearest
hundredth.
|
|
|
50.
|
a. | 3.45, –1.16 | b. | –3.45, 1.16 | c. | 2.3, –2.3 | d. | 6.89,
–2.32 |
|
|
|
51.
|
a. | 0.42, –2.71 | b. | 2.71, –0.42 | c. | 35.43, –33.14 | d. | 5.42,
–2.95 |
|
|
|
52.
|
a. | 2.83, –2.83 | b. | 1.17, –1.17 | c. | 3.32, –3.32 | d. | 0.85,
–0.85 |
|
|
|
53.
|
a. | 2.45, –2.45 | b. | 1.15, –1.15 | c. | 0.87, –0.87 | d. | 2.83,
–2.83 |
|
|
|
54.
|
For which discriminant is the graph possible? 
|
|
|
Find the number of real number solutions for the equation.
|
|
|
55.
|
|
|
|
56.
|
|
|
|
57.
|
|
|
|
58.
|
Graph the set of points. Which model is most appropriate for the
set?
(–6, –1), (–3, 2), (–1, 4), (2, 7)
a. | 
linear | c. | 
exponential | b. | 
quadratic | d. | 
linear |
|
|
|
59.
|
Graph the set of points. Which model is most appropriate for the
set?
(–2, 10), (–1,1), (1, 1), (2, 10)
a. | 
quadratic | c. | 
linear | b. | 
quadratic | d. | 
exponential |
|
|
|
60.
|
Which kind of function best models the data in the table? Graph the data and
write an equation to model the data. a. | 
exponential; y = 3x
– 1 | c. | 
linear; y = –x –
1 | b. | 
quadratic; y = x2
– 1 | d. | 
linear; y = x – 1 |
|
|
|
61.
|
The table shows the estimated number of deer living in a forest over a five-year
period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation
to model the data. Year | Estimated Population | 0 | 91 | 1 | 70 | 2 | 54 | 3 | 42 | 4 | 32 | | |
a. | exponential;  | c. | quadratic;  | b. | linear;  | d. | quadratic;  |
|
|
|
62.
|
In an exponential model, the y values ____ decrease as the x
values increase.
a. | always | b. | sometimes | c. | never |
|
|
|
63.
|
The equation  ____ has at least one real number solution when n
> 0. a. | always | b. | sometimes | c. | never |
|
Short Answer
|
|
|
64.
|
Make a table of values and graph the quadratic function  . 
|
|
|
65.
|
An architect is designing an archway. The shape of the arch is described by the
three inequalities given. Make a graph of the arch.  ;  ;  
|
|
|
66.
|
Use a calculator to find  to the nearest hundredth.
|
|
|
67.
|
Solve  by graphing the related function. 
|
|
|
68.
|
a. Write an expression for the total area of the model below.  b. The total area is 110 m 2. Write an equation to find
x. c. Solve the equation by completing the square.
|
|
|
69.
|
The formula  models the height of a model rocket, where h is
the height in meters, t is the time in seconds and v is the initial vertical velocity
in meters per second. If the model rocket is fired at an initial vertical velocity of 80 meters per
second, will the rocket ever reach a height of 88 meters? Justify your answer.
|
|
|
70.
|
Graph the data in the table below. Which kind of function best models the data?
Write an equation to model the data. 
|
|
|
71.
|
Graph the data in the table below. Which kind of function best models the data?
Write an equation to model the data. 
|
|
|
72.
|
For the equation  , find all the values of j such that the equation
has two real number solutions. Show your work.
|
Essay
|
|
|
73.
|
Graph the quadratic functions  and  . Compare the shape and
position of the graphs.
|
|
|
74.
|
The perimeter of a rectangular concrete slab is 114 feet and its area is 702
square feet. Find the dimensions of the rectangle. a. Using
l for the length of the rectangle, write an expression for the width of the rectangle in terms
of l. ( Hint: Solve the formula  for w.) Show your
work. b. Write a quadratic equation using l, the expression you found in part (a),
and the area of the slab. c. Solve the quadratic equation. Use the two solutions to find
the dimensions of the rectangle.
|
|
|
75.
|
a. Which kind of function best models the
data?
b. Write an equation to model the data.
c. If the pattern shown in the
table continues, what is the value of y for x = 6? Round to the nearest hundredth if
necessary.
|
Other
|
|
|
Which method(s) would you choose to solve the equation? Justify your
reasoning.
|
|
|
76.
|
|
|
|
77.
|
|