Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Multiply. 
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2.
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Factor  .
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3.
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Solve the equation  by graphing the related function.
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4.
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The trajectory of a potato launched from a potato cannon on the ground at
an angle of 45 degrees with an initial speed of 65 meters per second can be modeled by the
parabola:  x –
0.0023 x2, where the x-axis is the ground. Find the height of the highest
point of the trajectory and the horizontal distance the potato travels before hitting the
ground.  a. | height: 21 m; distance: 218 m | c. | height: 435 m; distance: 109
m | b. | height: 109 m; distance: 435 m | d. | height: 218 m; distance: 21
m |
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5.
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Find the axis of symmetry of the graph of  .
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6.
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The fish population of Lake Collins is decreasing at a rate of 4% per year. In
2002 there were about 1,250 fish. Write an exponential decay function to model this situation. Then
find the population in 2008.
a. | 
The population in 2008 will be about 58
fish. | b. | 
The population in 2008 will be about 300
fish. | c. | 
The population in 2008 will be about 978
fish. | d. | 
The population in 2008 will be about
978.45 fish. |
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7.
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Factor the trinomial  .
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8.
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Tell whether the polynomial  is completely factored. If
not, factor it. a. | No;  . | c. | No;  . | b. | No;  . | d. | Yes. |
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9.
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A radioactive isotope has a half-life of 13 hours. Find the amount of the
isotope left from a 400-milligram sample after 52 hours. If necessary, round your answer to the
nearest thousandth.
a. | 12.5 mg | c. | 25 mg | b. | 7.692 mg | d. | 0.049 mg |
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10.
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Factor the trinomial  .
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11.
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A golfer hits the golf ball. The quadratic function  gives the
time x seconds when the golf ball is at height 0 feet. How long does it take for the golf ball
to return to the ground? a. | 16 sec | c. | 5 sec | b. | 10 sec | d. | 80 sec |
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12.
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A rectangular picture measuring 5 in. by 9 in. is surrounded by a frame with
uniform width x. Write a quadratic function in standard form to show the combined area of the
picture and frame.
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13.
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The height of a soccer ball that is kicked from the ground can be approximated
by the function  , where y is the height of the soccer
ball in feet x seconds after it is kicked. Graph this function. Find the time it takes the
soccer ball to reach its maximum height, the soccer ball’s maximum height, and the time it
takes the soccer ball to return to the ground. a. | 
It takes the ball 3 seconds to reach its
maximum height. The ball’s maximum height is 36 feet. It takes the ball 3 seconds to return to
the ground. | c. | 
It takes the ball 1.5 seconds to reach its
maximum height. The ball’s maximum height is 36 feet. It takes the ball 1.5 seconds to return
to the ground. | b. | 
It takes the ball 36 seconds to reach its
maximum height. The ball’s maximum height is 3 feet. It takes the ball 36 seconds to return to
the ground. | d. | 
It takes the ball 1.5 seconds to reach its maximum height. The ball’s maximum
height is 36 feet. It takes the ball 3 seconds to return to the
ground. |
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14.
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Tell whether the function  is exponential. Explain your
answer. a. | Exponential function.
As the x-values are increased by a constant amount,
the y-values are multiplied by a constant amount. | b. | Not an exponential
function.
As the x-values are increased by a constant amount, the y-values increase
by the same amount. | c. | Exponential function.
As the x-values
are increased by a constant amount, the y-values increase by the same
amount. | d. | Not an exponential function.
As the x-values are increased by a constant
amount, the y-values are not multiplied by a constant amount. |
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15.
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Solve the quadratic equation  by factoring. a. | –4 and 2 | c. | 4 and –2 | b. | 4 and 2 | d. | –4 and
–2 |
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16.
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Find the vertex of the parabola  .  a. | (2, –3) | c. | (–2, 0) and (–4, 0) | b. | (–3,
2) | d. | (3,
–70) |
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17.
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Determine whether  is a difference of two squares. If so,
factor it. If not, explain why. a. |  | b. |  | c. |  | d. | Not a difference of squares because –49n4 is not a perfect
square. |
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18.
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A computer is worth $4000 when it is new. After each year it is worth half what
it was the previous year. What will its worth be after 4 years? Round your answer to the nearest
dollar.
a. | $250 | c. | $500 | b. | $1000 | d. | $125 |
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19.
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Graph y = –(4)x.
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20.
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Find the axis of symmetry of the parabola. 
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21.
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A builder uses parallelogram-shaped stones as decoration around a
building’s windows. The stones come in many different sizes. Each stone has a base length of
x inches and a height of  inches. Write a polynomial to describe the
area of a stone. Then find the area of a stone that has a length of 6 units.  a. |  ; Area = 114 in2 | c. |  ;
Area = 139 in2 | b. |  ; Area = 19
in. | d. |  ;
Area = 114 in2 |
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22.
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The function  , where x is the time in years, models a
declining lemming population. How many lemmings will there be in 6 years? a. | About 29,160 lemmings | c. | About 30,006 lemmings | b. | About 4,217
lemmings | d. | About 5,001
lemmings |
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23.
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The value of a gold coin picturing the head of the Roman Emperor Vespasian is
increasing at the rate of 5% per year. If the coin is worth $105 now, what
will it be worth in 11 years?
a. | $160.00 | c. | $179.59 | b. | $162.75 | d. | $169.79 |
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24.
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Factor  completely.
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25.
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Multiply. 
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26.
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A kicker starts a football game by “kicking off”. The quadratic
function  models the football’s height after x
seconds. How long is the football in the air? a. | 15 sec | c. | 3.75 sec | b. | 6.63 sec | d. | 1.94 sec |
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27.
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Tell whether the function  is quadratic.
Explain. a. | This is not a quadratic function because the x-term is
missing. | b. | This is not a quadratic function because it is not written in standard
form. | c. | This is a quadratic function because it has an 
term. | d. | This is a quadratic function because it can be written in standard form as  . |
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28.
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Factor  . Check that the original polynomial and the
factored form have the same values for x = 0, 1, 2, 3, and 4. a. | (x + 2)(x + 18) | c. | (x + 4)(x +
9) | b. | (x + 20)(x + 36) | d. | (x + 10)(x +
10) |
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29.
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Graph  .
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30.
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Use the information in the table to predict the number of termites in the
termite colony after one year. Termite Colony
Population | Time (months) | Number of
Termites | 0 | 20 | 1 | 80 | 2 | 320 | 3 | 1,280 | | |
a. | 335,544,320 termites | c. | 9,920 termites | b. | 5,120 termites | d. | 16,777,216
termites |
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31.
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Use the Zero Product Property to solve the equation  . a. | The solutions are –2 and 1. | c. | The solutions are 4 and
–3. | b. | The solutions are –4 and 3. | d. | The solutions are 2 and
–1. |
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32.
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Tell whether the graph of the quadratic function  opens upward
or downward. Explain. a. | Because  , the parabola opens
downward. | b. | Because  , the parabola opens
downward. | c. | Because  , the parabola opens
upward. | d. | Because  , the parabola opens
upward. |
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33.
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Factor the trinomial  .
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34.
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Identify the vertex of the parabola. Then give the minimum or maximum value of
the function.  a. | The vertex is  , and the maximum is 6. | b. | The vertex is  , and the minimum is 6. | c. | The vertex is  , and the
minimum is 3. | d. | The vertex is  , and the maximum is
3. |
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35.
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Find the zeros of the quadratic function  from the
graph.  a. | –8 | c. | 2 and –8 | b. | 1.5 | d. | 4 and –1 |
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36.
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A realtor estimates that a certain new house worth $500,000 will gain value at a
rate of 6% per year. Make a table that shows the worth of the house for years 0, 1, 2, 3, and 4. What
is the real-world meaning of year 0? Which type of model best represents the data in your table?
Explain. Write a function for the data.
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37.
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In the year 2000, the population of Mexico was about 100 million, and it was
growing by 1.53% per year. At this growth rate, the function  gives the
population, in millions, x years after 2000. Using this model, in what year would the
population reach 111 million? Round your answer to the nearest year.
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38.
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Factor  .
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39.
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Multiply. 
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40.
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Multiply. 
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41.
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Write a polynomial to represent the area of the shaded region. Then solve for
x given that the area of the shaded region is 24 square units. 
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42.
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Graph  .
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43.
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The height of an arrow that is shot upward at an initial velocity of 40 meters
per second can be modeled by  , where h is the height in meters and
t is the time in seconds. Find the time it takes for the arrow to reach the ground. a. | 4 sec | c. | 8 sec | b. | 6 sec | d. | 2 sec |
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44.
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Write a polynomial that represents the volume of the prism using
x.
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45.
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Write a compound interest function to model the following situation. Then, find
the balance after the given number of years.
$17,400 invested at a rate of 2.5% compounded
annually; 8 years
a. |  ; $26,550,293 | c. |  ;
$21,200 | b. |  ; $391,826,318 | d. |  ;
$84,504 |
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46.
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The height of a curved support beam can be modeled by  . Find the height and width of the beam.  a. | height = 12 units; width = 120 units | b. | height = 25 units; width = 120
units | c. | height = 12 units; width = 60 units | d. | height = 25 units; width = 60
units |
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47.
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Graph  . Find the axis of symmetry and the
vertex.
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48.
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Factor  .
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49.
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Multiply. 
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50.
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Factor x2 + 101x + 100.
a. | (x + 5)(x + 20) | c. | (x + 2)(x +
50) | b. | (x + 1)(x + 100) | d. | (x + 101)(x +
100) |
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