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Deck 5: Quadratic Functions and Models
Full screen (f)
Question
The quadratic function 
has a vertex at 
.
has a vertex at .
Question
The vertex of 
is 
.
is . Question
The equation 
has 2 real solutions.
has 2 real solutions. Question
is a factor of the perfect square 
. Question
Which one of the following graphs illustrate the function 
?
A)
B)
C) None of these options
D)
E)
?A)
B)
C) None of these options
D)
E)
Question
The graph of 
is obtained from the graph of 
by shifting the graph left 5 units.
is obtained from the graph of by shifting the graph left 5 units. Question
The graph of 
opens upward.
opens upward. Question
Which one of the following graphs illustrate the function 
?
A)
B)
C) None of these options
D)
E)
?A)
B)
C) None of these options
D)
E)
Question
The quadratic function 
has a maximum value at 
when 
.
has a maximum value at when . Question
Which one of the following functions translates the graph of 
to a new graph g with a vertical shift down 3 units and a horizontal shift left 8 units.
A)
B)
C)
D)
E)
to a new graph g with a vertical shift down 3 units and a horizontal shift left 8 units.A)
B)
C)
D)
E)
Question
A function f is given by the table. Find . 
A) 3
B) -1
C) 4
D) -4
E) 0
A) 3
B) -1
C) 4
D) -4
E) 0
Question
Which one of the following graphs illustrate the function 
?
A)
B)
C) None of these options
D)
E)
?A)
B)
C) None of these options
D)
E)
Question
The minimum value of the quadratic function 
occurs when 
.
occurs when . Question
The quadratic function 
has a maximum value at 
.
has a maximum value at . Question
Which one of the following functions translates the graph of 
to a new graph g with a reflection about the x -axis, a vertical stretch by a factor of 6, and a horizontal shift left 5 units.
A)
B)
C)
D)
E)
to a new graph g with a reflection about the x -axis, a vertical stretch by a factor of 6, and a horizontal shift left 5 units.A)
B)
C)
D)
E)
Question
Question
In the equation 
, the value of a is 
, the value of b is 7 and the value of c is 4.
, the value of a is , the value of b is 7 and the value of c is 4. Question
Question
Which one of the following graphs illustrate the function 
?
A)
B)
C)
D)
E)
?A)
B)
C)
D)
E)
Question
Let 
and let 
. If 
, then the number of x -intercepts for the graph of f is 0.
and let . If , then the number of x -intercepts for the graph of f is 0. Question
Given the function 
, find the average rate of change between 
and 
.
A) 0.05
B) 21
C) 7
D) 147
E) -3
, find the average rate of change between and .A) 0.05
B) 21
C) 7
D) 147
E) -3
Question
Using the graph below, find the y -value at which the minimum value of the function occurs. 
A)
B)
C)
D)
2
E)
A)
B)
C)
D)
2E)
Question
Using the graph below, find the x -value at which the minimum value of the function occurs. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 500 m apart, and the lowest point of the suspension cables is 120 m below the top of the towers, as shown below. Find a quadratic function that models the parabolic part of the cables, placing the origin of the coordinate axes at the vertex. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If 
represents Mark s driving distance (in miles) after t minutes on the road, which one of the following would describe the meaning of 
?
A) Not enough information.
B) Mark's driving distance plus an additional 5 miles.
C) Mark's driving distance after traveling for 5 minutes.
D) Mark s driving distance while traveling
miles per minute.
E) Mark s time driving on the road is
minutes.
represents Mark s driving distance (in miles) after t minutes on the road, which one of the following would describe the meaning of ?A) Not enough information.
B) Mark's driving distance plus an additional 5 miles.
C) Mark's driving distance after traveling for 5 minutes.
D) Mark s driving distance while traveling
miles per minute.E) Mark s time driving on the road is
minutes. Question
Using the graph below, find the x -value at which the maximum value of the function occurs. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the vertex of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Express 
in the standard form of a quadratic function.
A)
B)
C)
D)
E)
in the standard form of a quadratic function.A)
B)
C)
D)
E)
Question
Find the minimum value and the corresponding x -value at which the minimum occurs for the function 
.
A) Minimum value of 5 occurs when
B) Minimum value of
occurs when 
C) Minimum value of
occurs when 
D) Minimum value of 1 occurs when
E) Minimum value of 1 occurs when
.A) Minimum value of 5 occurs when
B) Minimum value of
occurs when C) Minimum value of
occurs when D) Minimum value of 1 occurs when
E) Minimum value of 1 occurs when
Question
A function f is given by the table. Find when . 
A) 5
B) -4
C) 8
D) 0
E) -2
A) 5
B) -4
C) 8
D) 0
E) -2
Question
Which one of the following functions describes a function f whose graph is a parabola with the vertex 
and passes through the point 
?
A)
B)
C)
D) f(x) =
E) f(x) =
and passes through the point ?A)
B)
C)
D) f(x) =
E) f(x) =
Question
Express 
in the general form of a quadratic function.
A)
B)
C)
D)
E)
in the general form of a quadratic function.A)
B)
C)
D)
E)
Question
Using the graph below, find the y -value at which the maximum value of the function occurs. 
A)
7
B)
2
C)
D)
E)
2
A)
7B)
2C)
D)
E)
2 Question
If 
represents John s salary per month (in thousands of dollars) after working 
number of months at a certain job, which one of the following would describe the meaning of 
?
A) John s salary after working
months at the job.
B) John's raise of $3 per month.
C) John's salary after working 3 months at the job.
D) Not enough information.
E) John's total number of months working at the job.
represents John s salary per month (in thousands of dollars) after working number of months at a certain job, which one of the following would describe the meaning of ?A) John s salary after working
months at the job.B) John's raise of $3 per month.
C) John's salary after working 3 months at the job.
D) Not enough information.
E) John's total number of months working at the job.
Question
Find the vertex of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the maximum or minimum value of the quadratic function 
.
A) The maximum value is
.
B) The maximum value is
.
C) The minimum value is 7.
D) The minimum value is
.
E) The minimum value is
.
.A) The maximum value is
.B) The maximum value is
.C) The minimum value is 7.
D) The minimum value is
.E) The minimum value is
. Question
Find a quadratic function g whose graph is shown below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The graph of g is given below and represents a transformation of the graph of 
. Which one of the functions best describes the graph of g . 
A)
B)
C)
D)
E)
. Which one of the functions best describes the graph of g . A)
B)
C)
D)
E)
Question
The graph of g is given below and represents a translation of the graph of 
. Which one of the functions best describes the graph of g . 
A)
B)
C)
D)
E)
. Which one of the functions best describes the graph of g . A)
B)
C)
D)
E)
Question
Express 
in the standard form of a quadratic function.
A)
B)
C)
D)
E)
in the standard form of a quadratic function.A)
B)
C)
D)
E)
Question
Solve the equation 
using the Quadratic Formula.
A)
B)
C)
D)
E)
and 
using the Quadratic Formula.A)
B)
C)
D)
E)
and Question
The number of oranges produced by each tree in an orange grove depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces 
oranges. So the number of oranges produced per acre is 
What is the maximum yield of the trees, and how many trees should be planted per acre to obtain the maximum yield of oranges? (Rounded to the nearest whole number)
A) Maximum yield of the trees is 625 oranges when 9 trees are planted
B) Maximum yield of the trees is 10,851 oranges when 35 trees are planted
C) There is no maximum yield of the trees
D) Maximum yield of the trees is 7,350 oranges when 15 trees are planted
E) Maximum yield of the trees is 27,500 oranges when 100 trees are planted
oranges. So the number of oranges produced per acre is What is the maximum yield of the trees, and how many trees should be planted per acre to obtain the maximum yield of oranges? (Rounded to the nearest whole number)A) Maximum yield of the trees is 625 oranges when 9 trees are planted
B) Maximum yield of the trees is 10,851 oranges when 35 trees are planted
C) There is no maximum yield of the trees
D) Maximum yield of the trees is 7,350 oranges when 15 trees are planted
E) Maximum yield of the trees is 27,500 oranges when 100 trees are planted
Question
Find the discriminant of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Solve the equation 
by factoring.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
by factoring.A)
and B)
and C)
and D)
and E)
and Question
A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by 
. What is the average rate of change of the height of the ball between 
seconds and 
seconds?
A) 0.3 ft/sec
B) 42.40 ft/sec
C) 115 ft/sec
D) 136.44 ft/sec
E) 213.09 ft/sec
. What is the average rate of change of the height of the ball between seconds and seconds?A) 0.3 ft/sec
B) 42.40 ft/sec
C) 115 ft/sec
D) 136.44 ft/sec
E) 213.09 ft/sec
Question
Solve the equation 
by factoring.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
by factoring.A)
and B)
and C)
and D)
and E)
and Question
Which one of the following is the graph for the function 
?
A)
B)
C) None of these options
D)
E)
?A)
B)
C) None of these options
D)
E)
Question
Find the discriminant of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
For the graph below, find the solution(s) to the equation 
. 
A)
and 
B)
C)
and 
D)
and 
E)
and 
. A)
and B)
C)
and D)
and E)
and Question
Solve the equation 
using the Quadratic Formula.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
using the Quadratic Formula.A)
and B)
and C)
and D)
and E)
and Question
Find the equation that represents the function graphed below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the equation 
using the Quadratic Formula.
A)
B)
and 
C)
D)
and 
E)
using the Quadratic Formula.A)
B)
and C)
D)
and E)
Question
Sam has 600 ft of fencing to fence in a rectangular garden. Find a function A that models the area of the garden in terms of the width of the garden and determine the maximum area of the garden and the corresponding width of the garden to attain this maximum area.
A)
; Maximum area of 67,500 square feet occurs for a garden of width 150 ft
B)
; Maximum area of 300 square feet occurs for a garden of width 299.00 ft
C)
; Maximum area of 300 square feet occurs for a garden of width 0 ft
D)
; Maximum area of 45,000 square feet occurs for a garden of width 150 ft
E)
; Maximum area of 22,500 square feet occurs for a garden of width 150 ft
A)
; Maximum area of 67,500 square feet occurs for a garden of width 150 ftB)
; Maximum area of 300 square feet occurs for a garden of width 299.00 ftC)
; Maximum area of 300 square feet occurs for a garden of width 0 ftD)
; Maximum area of 45,000 square feet occurs for a garden of width 150 ftE)
; Maximum area of 22,500 square feet occurs for a garden of width 150 ft Question
A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by 
. What is the maximum height attained by the ball, and after how many seconds is that height attained?
A) Maximum height of the ball is 160 ft after 2 seconds
B) Maximum height of the ball is
ft after 
seconds
C) Maximum height of the ball is 130 ft after 0.5 seconds
D) Maximum height of the ball is
ft after 1 seconds
E) Maximum height of the ball is 104 ft after 0 seconds
. What is the maximum height attained by the ball, and after how many seconds is that height attained?A) Maximum height of the ball is 160 ft after 2 seconds
B) Maximum height of the ball is
ft after secondsC) Maximum height of the ball is 130 ft after 0.5 seconds
D) Maximum height of the ball is
ft after 1 secondsE) Maximum height of the ball is 104 ft after 0 seconds
Question
Which one of the following is the graph for the function 
?
A)
B)
C)
D)
E)
?A)
B)
C)
D)
E)
Question
Find the maximum value and the corresponding x -value at which the maximum occurs for the function 
.
A) Maximum value of 12 occurs when
B) Maximum value of 28 occurs when
12
C) Maximum value of 4 occurs when
0
D) Maximum value of 12 occurs when
28
E) Maximum value of 28 occurs when
.A) Maximum value of 12 occurs when
B) Maximum value of 28 occurs when
12C) Maximum value of 4 occurs when
0D) Maximum value of 12 occurs when
28E) Maximum value of 28 occurs when
Question
Solve the equation 
by factoring.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
by factoring.A)
and B)
and C)
and D)
and E)
and Question
Using the graph below, choose the correct answer for the x -intercept(s), y -intercept, and vertex. 
A) x -intercepts are
and 
; y -intercept is 
; vertex is 
B) x -intercepts are
and 
; y -intercept is 
; vertex is 
C) x -intercepts are
and 
; y -intercept is 
; vertex is 
D) x -intercepts are
and 
; there are no y -intercepts; vertex is 
E) x -intercept is
; y -intercept is 
; vertex is 
A) x -intercepts are
and ; y -intercept is ; vertex is B) x -intercepts are
and ; y -intercept is ; vertex is C) x -intercepts are
and ; y -intercept is ; vertex is D) x -intercepts are
and ; there are no y -intercepts; vertex is E) x -intercept is
; y -intercept is ; vertex is Question
Find the discriminant of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Solve the equation 
using the Quadratic Formula. Round answers to nearest hundredth.
A)
and 
B) No real solutions
C)
and 
D)
and 
E)
and 
using the Quadratic Formula. Round answers to nearest hundredth.A)
and B) No real solutions
C)
and D)
and E)
and Question
A rectangular parking lot is 20 feet longer than it is wide. Which one of the following functions model the area of the lot?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by 
. Does the ball reach a height of 251 feet?
. Does the ball reach a height of 251 feet? Question
The following table shows the values of the number of gallons of water used by a family during the month of July.
Find the quadratic model based on the data provided that determines the number of gallons of water used as a function of the day. (Rounded to the nearest hundredth)
A)
B) Not enough information.
C)
D)
E)
Find the quadratic model based on the data provided that determines the number of gallons of water used as a function of the day. (Rounded to the nearest hundredth)
A)
B) Not enough information.
C)
D)
E)
Question
Express 
in the general form of a quadratic function.
A)
B)
C)
D)
E)
in the general form of a quadratic function.A)
B)
C)
D)
E)
Question
A penny is dropped from a high-rise building that is 350 feet high. After 8.4 seconds, the penny hits the ground. Which one of the following quadratic models describe the height of the penny above ground as a function of the time elapsed since the penny was dropped?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A diver jumps off the springboard and dives into a pool. The following table shows the distance of the diver from the surface of the water as a function of the time (in seconds) it takes for the diver to enter the water of the pool. 
Which one of the following is an appropriate scatterplot for this data?
A)
B)
C)
D)
E) None of these options
Which one of the following is an appropriate scatterplot for this data?A)
B)
C)
D)
E) None of these options
Question
A diver jumps off the springboard and dives into a pool. The following table shows the distance of the diver from the surface of the water as a function of the time (in seconds) it takes for the diver to enter the water of the pool.
Which one of the following is the quadratic model that best fits the data provided? (Rounded to the nearest tenth)
A)
B) Not enough information.
C)
D)
E)
Which one of the following is the quadratic model that best fits the data provided? (Rounded to the nearest tenth)A)
B) Not enough information.
C)
D)
E)
Question
Question
Using the data provided, create a quadratic model that best fits the data. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Based on the quadratic model that best fits the data, find the value of y when x is 6.8. (Rounded to the nearest hundredth) 
A) 99.72
B) 72.00
C) 72.50
D) 254.23
E) 110.38
A) 99.72
B) 72.00
C) 72.50
D) 254.23
E) 110.38
Question
A diver jumps off the springboard and dives into a pool. The following table shows the distance of the diver from the surface of the water as a function of the time (in seconds) it takes for the diver to enter the water of the pool.
Based on a quadratic regression model, when will the diver enter the water? (Rounded to the nearest tenth)
A) After 2.8 seconds
B) After 2.6 seconds
C) After 2.9 seconds
D) After 2.7 seconds
E) After 3.0 seconds
Based on a quadratic regression model, when will the diver enter the water? (Rounded to the nearest tenth)
A) After 2.8 seconds
B) After 2.6 seconds
C) After 2.9 seconds
D) After 2.7 seconds
E) After 3.0 seconds
Question
A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by 
. When does the ball hit the ground?
A) The ball never hits the ground.
B) After 5.79 seconds
C) After 1.29 seconds
D) After 3 seconds
E) After 0 seconds
. When does the ball hit the ground?A) The ball never hits the ground.
B) After 5.79 seconds
C) After 1.29 seconds
D) After 3 seconds
E) After 0 seconds
Question
Is a quadratic function an appropriate model for the following data?
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Deck 5: Quadratic Functions and Models
1
The quadratic function has a vertex at .
has a vertex at .True
2
The vertex of is .
is .True
3
The equation has 2 real solutions.
has 2 real solutions.False
4
is a factor of the perfect square . Unlock Deck
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5
Which one of the following graphs illustrate the function ?
A)
B)
C) None of these options
D)
E)
?A)
B)
C) None of these options
D)
E)
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6
The graph of is obtained from the graph of by shifting the graph left 5 units.
is obtained from the graph of by shifting the graph left 5 units. Unlock Deck
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7
The graph of opens upward.
opens upward. Unlock Deck
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8
Which one of the following graphs illustrate the function ?
A)
B)
C) None of these options
D)
E)
?A)
B)
C) None of these options
D)
E)
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9
The quadratic function has a maximum value at when .
has a maximum value at when . Unlock Deck
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10
Which one of the following functions translates the graph of to a new graph g with a vertical shift down 3 units and a horizontal shift left 8 units.
A)
B)
C)
D)
E)
to a new graph g with a vertical shift down 3 units and a horizontal shift left 8 units.A)
B)
C)
D)
E)
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11
A function f is given by the table. Find .
A) 3
B) -1
C) 4
D) -4
E) 0
A) 3
B) -1
C) 4
D) -4
E) 0
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12
Which one of the following graphs illustrate the function ?
A)
B)
C) None of these options
D)
E)
?A)
B)
C) None of these options
D)
E)
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13
The minimum value of the quadratic function occurs when .
occurs when . Unlock Deck
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14
The quadratic function has a maximum value at .
has a maximum value at . Unlock Deck
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15
Which one of the following functions translates the graph of to a new graph g with a reflection about the x -axis, a vertical stretch by a factor of 6, and a horizontal shift left 5 units.
A)
B)
C)
D)
E)
to a new graph g with a reflection about the x -axis, a vertical stretch by a factor of 6, and a horizontal shift left 5 units.A)
B)
C)
D)
E)
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16
If the y -values of a set of data decrease by 7 for each increase of 1 in the x -values, a quadratic function may be appropriate to model the data.
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17
In the equation , the value of a is , the value of b is 7 and the value of c is 4.
, the value of a is , the value of b is 7 and the value of c is 4. Unlock Deck
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18
If the y -values of a set of data increase by different amounts when the x -values increase by the value of 6, then a linear function will best model the data.
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19
Which one of the following graphs illustrate the function ?
A)
B)
C)
D)
E)
?A)
B)
C)
D)
E)
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20
Let and let . If , then the number of x -intercepts for the graph of f is 0.
and let . If , then the number of x -intercepts for the graph of f is 0. Unlock Deck
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21
Given the function , find the average rate of change between and .
A) 0.05
B) 21
C) 7
D) 147
E) -3
, find the average rate of change between and .A) 0.05
B) 21
C) 7
D) 147
E) -3
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22
Using the graph below, find the y -value at which the minimum value of the function occurs.
A)
B)
C)
D) 2
E)
A)
B)
C)
D)
2E)
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23
Using the graph below, find the x -value at which the minimum value of the function occurs.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 500 m apart, and the lowest point of the suspension cables is 120 m below the top of the towers, as shown below. Find a quadratic function that models the parabolic part of the cables, placing the origin of the coordinate axes at the vertex.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
If represents Mark s driving distance (in miles) after t minutes on the road, which one of the following would describe the meaning of ?
A) Not enough information.
B) Mark's driving distance plus an additional 5 miles.
C) Mark's driving distance after traveling for 5 minutes.
D) Mark s driving distance while traveling miles per minute.
E) Mark s time driving on the road is minutes.
represents Mark s driving distance (in miles) after t minutes on the road, which one of the following would describe the meaning of ?A) Not enough information.
B) Mark's driving distance plus an additional 5 miles.
C) Mark's driving distance after traveling for 5 minutes.
D) Mark s driving distance while traveling
miles per minute.E) Mark s time driving on the road is
minutes. Unlock Deck
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26
Using the graph below, find the x -value at which the maximum value of the function occurs.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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27
Find the vertex of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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28
Express in the standard form of a quadratic function.
A)
B)
C)
D)
E)
in the standard form of a quadratic function.A)
B)
C)
D)
E)
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29
Find the minimum value and the corresponding x -value at which the minimum occurs for the function .
A) Minimum value of 5 occurs when
B) Minimum value of occurs when
C) Minimum value of occurs when
D) Minimum value of 1 occurs when
E) Minimum value of 1 occurs when
.A) Minimum value of 5 occurs when
B) Minimum value of
occurs when C) Minimum value of
occurs when D) Minimum value of 1 occurs when
E) Minimum value of 1 occurs when
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30
A function f is given by the table. Find when .
A) 5
B) -4
C) 8
D) 0
E) -2
A) 5
B) -4
C) 8
D) 0
E) -2
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31
Which one of the following functions describes a function f whose graph is a parabola with the vertex and passes through the point ?
A)
B)
C)
D) f(x) =
E) f(x) =
and passes through the point ?A)
B)
C)
D) f(x) =
E) f(x) =
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32
Express in the general form of a quadratic function.
A)
B)
C)
D)
E)
in the general form of a quadratic function.A)
B)
C)
D)
E)
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33
Using the graph below, find the y -value at which the maximum value of the function occurs.
A) 7
B) 2
C)
D)
E) 2
A)
7B)
2C)
D)
E)
2 Unlock Deck
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34
If represents John s salary per month (in thousands of dollars) after working number of months at a certain job, which one of the following would describe the meaning of ?
A) John s salary after working months at the job.
B) John's raise of $3 per month.
C) John's salary after working 3 months at the job.
D) Not enough information.
E) John's total number of months working at the job.
represents John s salary per month (in thousands of dollars) after working number of months at a certain job, which one of the following would describe the meaning of ?A) John s salary after working
months at the job.B) John's raise of $3 per month.
C) John's salary after working 3 months at the job.
D) Not enough information.
E) John's total number of months working at the job.
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35
Find the vertex of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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36
Find the maximum or minimum value of the quadratic function .
A) The maximum value is .
B) The maximum value is .
C) The minimum value is 7.
D) The minimum value is .
E) The minimum value is .
.A) The maximum value is
.B) The maximum value is
.C) The minimum value is 7.
D) The minimum value is
.E) The minimum value is
. Unlock Deck
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37
Find a quadratic function g whose graph is shown below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
The graph of g is given below and represents a transformation of the graph of . Which one of the functions best describes the graph of g .
A)
B)
C)
D)
E)
. Which one of the functions best describes the graph of g . A)
B)
C)
D)
E)
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39
The graph of g is given below and represents a translation of the graph of . Which one of the functions best describes the graph of g .
A)
B)
C)
D)
E)
. Which one of the functions best describes the graph of g . A)
B)
C)
D)
E)
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40
Express in the standard form of a quadratic function.
A)
B)
C)
D)
E)
in the standard form of a quadratic function.A)
B)
C)
D)
E)
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41
Solve the equation using the Quadratic Formula.
A)
B)
C)
D)
E) and
using the Quadratic Formula.A)
B)
C)
D)
E)
and Unlock Deck
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42
The number of oranges produced by each tree in an orange grove depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces oranges. So the number of oranges produced per acre is What is the maximum yield of the trees, and how many trees should be planted per acre to obtain the maximum yield of oranges? (Rounded to the nearest whole number)
A) Maximum yield of the trees is 625 oranges when 9 trees are planted
B) Maximum yield of the trees is 10,851 oranges when 35 trees are planted
C) There is no maximum yield of the trees
D) Maximum yield of the trees is 7,350 oranges when 15 trees are planted
E) Maximum yield of the trees is 27,500 oranges when 100 trees are planted
oranges. So the number of oranges produced per acre is What is the maximum yield of the trees, and how many trees should be planted per acre to obtain the maximum yield of oranges? (Rounded to the nearest whole number)A) Maximum yield of the trees is 625 oranges when 9 trees are planted
B) Maximum yield of the trees is 10,851 oranges when 35 trees are planted
C) There is no maximum yield of the trees
D) Maximum yield of the trees is 7,350 oranges when 15 trees are planted
E) Maximum yield of the trees is 27,500 oranges when 100 trees are planted
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43
Find the discriminant of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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44
Solve the equation by factoring.
A) and
B) and
C) and
D) and
E) and
by factoring.A)
and B)
and C)
and D)
and E)
and Unlock Deck
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45
A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by . What is the average rate of change of the height of the ball between seconds and seconds?
A) 0.3 ft/sec
B) 42.40 ft/sec
C) 115 ft/sec
D) 136.44 ft/sec
E) 213.09 ft/sec
. What is the average rate of change of the height of the ball between seconds and seconds?A) 0.3 ft/sec
B) 42.40 ft/sec
C) 115 ft/sec
D) 136.44 ft/sec
E) 213.09 ft/sec
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46
Solve the equation by factoring.
A) and
B) and
C) and
D) and
E) and
by factoring.A)
and B)
and C)
and D)
and E)
and Unlock Deck
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47
Which one of the following is the graph for the function ?
A)
B)
C) None of these options
D)
E)
?A)
B)
C) None of these options
D)
E)
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48
Find the discriminant of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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49
For the graph below, find the solution(s) to the equation .
A) and
B)
C) and
D) and
E) and
. A)
and B)
C)
and D)
and E)
and Unlock Deck
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50
Solve the equation using the Quadratic Formula.
A) and
B) and
C) and
D) and
E) and
using the Quadratic Formula.A)
and B)
and C)
and D)
and E)
and Unlock Deck
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51
Find the equation that represents the function graphed below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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52
Solve the equation using the Quadratic Formula.
A)
B) and
C)
D) and
E)
using the Quadratic Formula.A)
B)
and C)
D)
and E)
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53
Sam has 600 ft of fencing to fence in a rectangular garden. Find a function A that models the area of the garden in terms of the width of the garden and determine the maximum area of the garden and the corresponding width of the garden to attain this maximum area.
A) ; Maximum area of 67,500 square feet occurs for a garden of width 150 ft
B) ; Maximum area of 300 square feet occurs for a garden of width 299.00 ft
C) ; Maximum area of 300 square feet occurs for a garden of width 0 ft
D) ; Maximum area of 45,000 square feet occurs for a garden of width 150 ft
E) ; Maximum area of 22,500 square feet occurs for a garden of width 150 ft
A)
; Maximum area of 67,500 square feet occurs for a garden of width 150 ftB)
; Maximum area of 300 square feet occurs for a garden of width 299.00 ftC)
; Maximum area of 300 square feet occurs for a garden of width 0 ftD)
; Maximum area of 45,000 square feet occurs for a garden of width 150 ftE)
; Maximum area of 22,500 square feet occurs for a garden of width 150 ft Unlock Deck
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54
A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by . What is the maximum height attained by the ball, and after how many seconds is that height attained?
A) Maximum height of the ball is 160 ft after 2 seconds
B) Maximum height of the ball is ft after seconds
C) Maximum height of the ball is 130 ft after 0.5 seconds
D) Maximum height of the ball is ft after 1 seconds
E) Maximum height of the ball is 104 ft after 0 seconds
. What is the maximum height attained by the ball, and after how many seconds is that height attained?A) Maximum height of the ball is 160 ft after 2 seconds
B) Maximum height of the ball is
ft after secondsC) Maximum height of the ball is 130 ft after 0.5 seconds
D) Maximum height of the ball is
ft after 1 secondsE) Maximum height of the ball is 104 ft after 0 seconds
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55
Which one of the following is the graph for the function ?
A)
B)
C)
D)
E)
?A)
B)
C)
D)
E)
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56
Find the maximum value and the corresponding x -value at which the maximum occurs for the function .
A) Maximum value of 12 occurs when
B) Maximum value of 28 occurs when 12
C) Maximum value of 4 occurs when 0
D) Maximum value of 12 occurs when 28
E) Maximum value of 28 occurs when
.A) Maximum value of 12 occurs when
B) Maximum value of 28 occurs when
12C) Maximum value of 4 occurs when
0D) Maximum value of 12 occurs when
28E) Maximum value of 28 occurs when
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57
Solve the equation by factoring.
A) and
B) and
C) and
D) and
E) and
by factoring.A)
and B)
and C)
and D)
and E)
and Unlock Deck
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58
Using the graph below, choose the correct answer for the x -intercept(s), y -intercept, and vertex.
A) x -intercepts are and ; y -intercept is ; vertex is
B) x -intercepts are and ; y -intercept is ; vertex is
C) x -intercepts are and ; y -intercept is ; vertex is
D) x -intercepts are and ; there are no y -intercepts; vertex is
E) x -intercept is ; y -intercept is ; vertex is
A) x -intercepts are
and ; y -intercept is ; vertex is B) x -intercepts are
and ; y -intercept is ; vertex is C) x -intercepts are
and ; y -intercept is ; vertex is D) x -intercepts are
and ; there are no y -intercepts; vertex is E) x -intercept is
; y -intercept is ; vertex is Unlock Deck
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59
Find the discriminant of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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60
Solve the equation using the Quadratic Formula. Round answers to nearest hundredth.
A) and
B) No real solutions
C) and
D) and
E) and
using the Quadratic Formula. Round answers to nearest hundredth.A)
and B) No real solutions
C)
and D)
and E)
and Unlock Deck
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61
A rectangular parking lot is 20 feet longer than it is wide. Which one of the following functions model the area of the lot?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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62
A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by . Does the ball reach a height of 251 feet?
. Does the ball reach a height of 251 feet? Unlock Deck
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63
The following table shows the values of the number of gallons of water used by a family during the month of July.
Find the quadratic model based on the data provided that determines the number of gallons of water used as a function of the day. (Rounded to the nearest hundredth)
A)
B) Not enough information.
C)
D)
E)
Find the quadratic model based on the data provided that determines the number of gallons of water used as a function of the day. (Rounded to the nearest hundredth)
A)
B) Not enough information.
C)
D)
E)
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64
Express in the general form of a quadratic function.
A)
B)
C)
D)
E)
in the general form of a quadratic function.A)
B)
C)
D)
E)
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65
A penny is dropped from a high-rise building that is 350 feet high. After 8.4 seconds, the penny hits the ground. Which one of the following quadratic models describe the height of the penny above ground as a function of the time elapsed since the penny was dropped?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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66
A diver jumps off the springboard and dives into a pool. The following table shows the distance of the diver from the surface of the water as a function of the time (in seconds) it takes for the diver to enter the water of the pool. Which one of the following is an appropriate scatterplot for this data?
A)
B)
C)
D)
E) None of these options
Which one of the following is an appropriate scatterplot for this data?A)
B)
C)
D)
E) None of these options
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67
A diver jumps off the springboard and dives into a pool. The following table shows the distance of the diver from the surface of the water as a function of the time (in seconds) it takes for the diver to enter the water of the pool.
Which one of the following is the quadratic model that best fits the data provided? (Rounded to the nearest tenth)
A)
B) Not enough information.
C)
D)
E)
Which one of the following is the quadratic model that best fits the data provided? (Rounded to the nearest tenth)A)
B) Not enough information.
C)
D)
E)
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68
A rectangular parking lot is 22 feet longer than it is wide. If the lot has an area of 9,000 square feet, then what are the dimensions of the lot?
A) The width of the parking lot is 84.5 ft and the length is 106.5 ft.
B) The width of the parking lot is 95 ft and the length is 100 ft.
C) The width of the parking lot is 78 ft and the length is 121.8 ft.
D) The width of the parking lot is 74.5 ft and the length is 127.5 ft.
E) The width of the parking lot is 89 ft and the length is 106.7 ft.
A) The width of the parking lot is 84.5 ft and the length is 106.5 ft.
B) The width of the parking lot is 95 ft and the length is 100 ft.
C) The width of the parking lot is 78 ft and the length is 121.8 ft.
D) The width of the parking lot is 74.5 ft and the length is 127.5 ft.
E) The width of the parking lot is 89 ft and the length is 106.7 ft.
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69
Using the data provided, create a quadratic model that best fits the data.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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70
Based on the quadratic model that best fits the data, find the value of y when x is 6.8. (Rounded to the nearest hundredth)
A) 99.72
B) 72.00
C) 72.50
D) 254.23
E) 110.38
A) 99.72
B) 72.00
C) 72.50
D) 254.23
E) 110.38
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71
A diver jumps off the springboard and dives into a pool. The following table shows the distance of the diver from the surface of the water as a function of the time (in seconds) it takes for the diver to enter the water of the pool.
Based on a quadratic regression model, when will the diver enter the water? (Rounded to the nearest tenth)
A) After 2.8 seconds
B) After 2.6 seconds
C) After 2.9 seconds
D) After 2.7 seconds
E) After 3.0 seconds
Based on a quadratic regression model, when will the diver enter the water? (Rounded to the nearest tenth)
A) After 2.8 seconds
B) After 2.6 seconds
C) After 2.9 seconds
D) After 2.7 seconds
E) After 3.0 seconds
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72
A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by . When does the ball hit the ground?
A) The ball never hits the ground.
B) After 5.79 seconds
C) After 1.29 seconds
D) After 3 seconds
E) After 0 seconds
. When does the ball hit the ground?A) The ball never hits the ground.
B) After 5.79 seconds
C) After 1.29 seconds
D) After 3 seconds
E) After 0 seconds
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73
Is a quadratic function an appropriate model for the following data?
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