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Deck 9: Quadratic Equations, Quadratic Functions, and Complex Numbers
Full screen (f)
Question
Factor the trinomial square and use the square root method to solve the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) irrational, unequal
D) rational, equal
E) irrational, equal
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) irrational, unequal
D) rational, equal
E) irrational, equal
Question
Factor the trinomial square and use the square root method to solve the equation. 
A)
, 
B)
, 
C)
, 
D)
, 
A)
, B)
, C)
, D)
, Question
Use the method of completing the square to solve the quadratic equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the method of completing the square to solve the quadratic equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
When a wholesaler sells 
CD players, the revenue is 
. How many CD players would the wholesaler have to sell to receive 
?
A)
CD players
B)
CD players
C)
CD players
D)
CD players
E)
CD players
CD players, the revenue is . How many CD players would the wholesaler have to sell to receive ?A)
CD playersB)
CD playersC)
CD playersD)
CD playersE)
CD players Question
Use the factoring method to solve the equation. 
A)
, 
B)
, 
C)
, 
D)
, 
E)
, 
A)
, B)
, C)
, D)
, E)
, Question
Solve the equation by completing the square. 
A)
, 
B)
, 
C)
, 
D)
, 
E)
, 
A)
, B)
, C)
, D)
, E)
, Question
The distance (in feet) that an object will fall in 
seconds is given by the formula 
. How long will it take an object to fall 784 feet?
A) 7 sec
B) 49 sec
C) 9 sec
D) 6 sec
E) 48 sec
seconds is given by the formula . How long will it take an object to fall 784 feet?A) 7 sec
B) 49 sec
C) 9 sec
D) 6 sec
E) 48 sec
Question
Use the square root method to solve the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the quadratic formula to find all real solutions of the equation. 
A) x = 10, x = 4
B) x = 5, x = -2
C) x = 5, x = 4
D) x = -5, x = 2
E) x = 5, x = 2
A) x = 10, x = 4
B) x = 5, x = -2
C) x = 5, x = 4
D) x = -5, x = 2
E) x = 5, x = 2
Question
The height in feet 
of a rocket in flight is given by the formula 
, where 
is the time of the flight in seconds. How long will it take for the rocket to hit the ground?
A) 11 sec
B) 10 sec
C) 8 sec
D) 12 sec
E) 13 sec
of a rocket in flight is given by the formula , where is the time of the flight in seconds. How long will it take for the rocket to hit the ground?A) 11 sec
B) 10 sec
C) 8 sec
D) 12 sec
E) 13 sec
Question
Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) rational, equal
D) irrational, unequal
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) rational, equal
D) irrational, unequal
Question
Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 
A) rational, equal
B) irrational, unequal
C) irrational, equal
D) nonreal complex numbers, complex conjugates
E) rational, unequal
A) rational, equal
B) irrational, unequal
C) irrational, equal
D) nonreal complex numbers, complex conjugates
E) rational, unequal
Question
What is the first step to solving x 2 
10 x = 56 by completing the square?
A) Add 25 to both sides.
B) Add -25 to both sides
C) Subtract 56 from both sides.
D) Isolate x 2 .
E) none of these
10 x = 56 by completing the square?A) Add 25 to both sides.
B) Add -25 to both sides
C) Subtract 56 from both sides.
D) Isolate x 2 .
E) none of these
Question
Complete the square and factor the resulting perfect-square trinomial. 
A) ( t + 16 )
B) ( t - 4 )
C) ( t + 4 )
D) ( t - 16 )
A) ( t + 16 )
B) ( t - 4 )
C) ( t + 4 )
D) ( t - 16 )
Question
Use the quadratic formula to find all real solutions of the equation. 
A)
B)
C)
D)
E) no real solutions
A)
B)
C)
D)
E) no real solutions
Question
Complete the square and factor the resulting perfect-square trinomial. 
A) ( 8 t +
) 
B) ( 8 t -
) 
C) ( 8 t +
) 
D) ( 8 t -
) 
A) ( 8 t +
) B) ( 8 t -
) C) ( 8 t +
) D) ( 8 t -
) Question
The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.
A) 16
B) 17
C) 16
D) 15
E) 8
A) 16
B) 17
C) 16
D) 15
E) 8
Question
Solve the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If the orbit of the comet is approximated by the equation 
, how far is it from the sun at the vertex of the orbit? Distances are measured in astronomical units (AU). 
A) 2 AU
B) 4 AU
C) 1 AU
D) 5 AU
E) 3 AU
, how far is it from the sun at the vertex of the orbit? Distances are measured in astronomical units (AU). A) 2 AU
B) 4 AU
C) 1 AU
D) 5 AU
E) 3 AU
Question
Simplify the expression. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
The cannonball in the illustration follows the parabolic trajectory 
. How far short of the castle does it land? 
A) 5 ft
B) 6 ft
C) 3 ft
D) 4 ft
E) 2 ft
. How far short of the castle does it land? A) 5 ft
B) 6 ft
C) 3 ft
D) 4 ft
E) 2 ft
Question
Find the minimum point of the graph of 
.
A)
B)
C)
D)
.A)
B)
C)
D)
Question
Find the vertex of the graph of the equation. Do not draw the graph. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
How many x -intercepts does the following parabola have? 
A) 0
B) 2
C) 1
A) 0
B) 2
C) 1
Question
Find the vertex of the graph of the equation. Do not draw the graph. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Use a graphing calculator to solve the equation. If an answer is not exact, give the result to the nearest hundredth. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
A wholesaler sells CD players for $170 each. However, she gives volume discounts on purchases of 100 to 1,500 units according to the formula 
, where n represents the number of units purchased. How many units would a retailer have to buy for the wholesaler to obtain maximum revenue?
A) 1,170 units
B) 850 units
C) 470 units
D) 550 units
E) 450 units
, where n represents the number of units purchased. How many units would a retailer have to buy for the wholesaler to obtain maximum revenue?A) 1,170 units
B) 850 units
C) 470 units
D) 550 units
E) 450 units
Question
Simplify the expression. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
The area of a tennis court is 2,128 square feet (see illustration). The length of the court is 
times the width. Find the length and width of the tennis court. 
A) 94 feet by 25 feet
B) 82 feet by 26 feet
C) 85 feet by 25 feet
D) 76 feet by 22 feet
E) 76 feet by 28 feet
times the width. Find the length and width of the tennis court. A) 94 feet by 25 feet
B) 82 feet by 26 feet
C) 85 feet by 25 feet
D) 76 feet by 22 feet
E) 76 feet by 28 feet
Question
Simplify: 
Question
Use a graphing calculator to solve the equation. If an answer is not exact, give the result to the nearest hundredth. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Graph the equation 
.
A)
B)
C)
D)
.A)
B)
C)
D)
Question
Question
Find the vertex of the graph of the equation. Do not draw the graph. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Graph the parabola and give the coordinates of the vertex. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write 
in terms of i and simplify.
A)
B)
C)
D)
E)
in terms of i and simplify.A)
B)
C)
D)
E)
Question
Construct a table of solutions and graph of 
.
A)
B)
C)
D)
.A)
B)
C)
D)
Question
Determine the vertex and axis of symmetry for 
.
A) vertex:
; axis: 
B) vertex:
; axis: 
C) vertex:
; axis: 
D) vertex:
; axis: 
.A) vertex:
; axis: B) vertex:
; axis: C) vertex:
; axis: D) vertex:
; axis: Question
Write the expression in 
form. 
A)
B)
C)
D)
E)
form. A)
B)
C)
D)
E)
Question
Solve the following quadratic equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write 
in terms of i and simplify.
A)
B)
C)
D)
E)
in terms of i and simplify.A)
B)
C)
D)
E)
Question
Solve the following quadratic equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the operation. Write the answer in a + bi form. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Write the expression in a + bi form. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Write 
in terms of i , perform the indicated operations, and simplify.
A)
B)
C)
D)
E)
in terms of i , perform the indicated operations, and simplify.A)
B)
C)
D)
E)
Question
Write the expression in a + bi form. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Simplify the expression. Enter the answer in a + bi form. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Simplify the expression. Enter the answer in a + bi form. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Solve the equation. Enter all roots in bi or a + bi form. 
A)
B)
C)
D)
A)
B)
C)
D)
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Full screen (f)
Deck 9: Quadratic Equations, Quadratic Functions, and Complex Numbers
1
Factor the trinomial square and use the square root method to solve the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) irrational, unequal
D) rational, equal
E) irrational, equal
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) irrational, unequal
D) rational, equal
E) irrational, equal
irrational, unequal
3
Factor the trinomial square and use the square root method to solve the equation.
A) ,
B) ,
C) ,
D) ,
A)
, B)
, C)
, D)
, , 4
Use the method of completing the square to solve the quadratic equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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5
Use the method of completing the square to solve the quadratic equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
6
When a wholesaler sells CD players, the revenue is . How many CD players would the wholesaler have to sell to receive ?
A) CD players
B) CD players
C) CD players
D) CD players
E) CD players
CD players, the revenue is . How many CD players would the wholesaler have to sell to receive ?A)
CD playersB)
CD playersC)
CD playersD)
CD playersE)
CD players Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
7
Use the factoring method to solve the equation.
A) ,
B) ,
C) ,
D) ,
E) ,
A)
, B)
, C)
, D)
, E)
, Unlock Deck
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k this deck
8
Solve the equation by completing the square.
A) ,
B) ,
C) ,
D) ,
E) ,
A)
, B)
, C)
, D)
, E)
, Unlock Deck
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Unlock Deck
k this deck
9
The distance (in feet) that an object will fall in seconds is given by the formula . How long will it take an object to fall 784 feet?
A) 7 sec
B) 49 sec
C) 9 sec
D) 6 sec
E) 48 sec
seconds is given by the formula . How long will it take an object to fall 784 feet?A) 7 sec
B) 49 sec
C) 9 sec
D) 6 sec
E) 48 sec
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
10
Use the square root method to solve the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
11
Use the quadratic formula to find all real solutions of the equation.
A) x = 10, x = 4
B) x = 5, x = -2
C) x = 5, x = 4
D) x = -5, x = 2
E) x = 5, x = 2
A) x = 10, x = 4
B) x = 5, x = -2
C) x = 5, x = 4
D) x = -5, x = 2
E) x = 5, x = 2
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k this deck
12
The height in feet of a rocket in flight is given by the formula , where is the time of the flight in seconds. How long will it take for the rocket to hit the ground?
A) 11 sec
B) 10 sec
C) 8 sec
D) 12 sec
E) 13 sec
of a rocket in flight is given by the formula , where is the time of the flight in seconds. How long will it take for the rocket to hit the ground?A) 11 sec
B) 10 sec
C) 8 sec
D) 12 sec
E) 13 sec
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
13
Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) rational, equal
D) irrational, unequal
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) rational, equal
D) irrational, unequal
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
14
Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.
A) rational, equal
B) irrational, unequal
C) irrational, equal
D) nonreal complex numbers, complex conjugates
E) rational, unequal
A) rational, equal
B) irrational, unequal
C) irrational, equal
D) nonreal complex numbers, complex conjugates
E) rational, unequal
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k this deck
15
What is the first step to solving x 2 10 x = 56 by completing the square?
A) Add 25 to both sides.
B) Add -25 to both sides
C) Subtract 56 from both sides.
D) Isolate x 2 .
E) none of these
10 x = 56 by completing the square?A) Add 25 to both sides.
B) Add -25 to both sides
C) Subtract 56 from both sides.
D) Isolate x 2 .
E) none of these
Unlock Deck
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k this deck
16
Complete the square and factor the resulting perfect-square trinomial.
A) ( t + 16 )
B) ( t - 4 )
C) ( t + 4 )
D) ( t - 16 )
A) ( t + 16 )
B) ( t - 4 )
C) ( t + 4 )
D) ( t - 16 )
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k this deck
17
Use the quadratic formula to find all real solutions of the equation.
A)
B)
C)
D)
E) no real solutions
A)
B)
C)
D)
E) no real solutions
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
18
Complete the square and factor the resulting perfect-square trinomial.
A) ( 8 t + )
B) ( 8 t - )
C) ( 8 t + )
D) ( 8 t - )
A) ( 8 t +
) B) ( 8 t -
) C) ( 8 t +
) D) ( 8 t -
) Unlock Deck
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k this deck
19
The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.
A) 16
B) 17
C) 16
D) 15
E) 8
A) 16
B) 17
C) 16
D) 15
E) 8
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k this deck
20
Solve the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
k this deck
21
If the orbit of the comet is approximated by the equation , how far is it from the sun at the vertex of the orbit? Distances are measured in astronomical units (AU).
A) 2 AU
B) 4 AU
C) 1 AU
D) 5 AU
E) 3 AU
, how far is it from the sun at the vertex of the orbit? Distances are measured in astronomical units (AU). A) 2 AU
B) 4 AU
C) 1 AU
D) 5 AU
E) 3 AU
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k this deck
22
Simplify the expression.
A)
B)
C)
D)
A)
B)
C)
D)
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23
The cannonball in the illustration follows the parabolic trajectory . How far short of the castle does it land?
A) 5 ft
B) 6 ft
C) 3 ft
D) 4 ft
E) 2 ft
. How far short of the castle does it land? A) 5 ft
B) 6 ft
C) 3 ft
D) 4 ft
E) 2 ft
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k this deck
24
Find the minimum point of the graph of .
A)
B)
C)
D)
.A)
B)
C)
D)
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25
Find the vertex of the graph of the equation. Do not draw the graph.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
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26
How many x -intercepts does the following parabola have?
A) 0
B) 2
C) 1
A) 0
B) 2
C) 1
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k this deck
27
Find the vertex of the graph of the equation. Do not draw the graph.
A)
B)
C)
D)
A)
B)
C)
D)
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28
Use a graphing calculator to solve the equation. If an answer is not exact, give the result to the nearest hundredth.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
29
A wholesaler sells CD players for $170 each. However, she gives volume discounts on purchases of 100 to 1,500 units according to the formula , where n represents the number of units purchased. How many units would a retailer have to buy for the wholesaler to obtain maximum revenue?
A) 1,170 units
B) 850 units
C) 470 units
D) 550 units
E) 450 units
, where n represents the number of units purchased. How many units would a retailer have to buy for the wholesaler to obtain maximum revenue?A) 1,170 units
B) 850 units
C) 470 units
D) 550 units
E) 450 units
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
30
Simplify the expression.
A)
B)
C)
D)
A)
B)
C)
D)
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Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
31
The area of a tennis court is 2,128 square feet (see illustration). The length of the court is times the width. Find the length and width of the tennis court.
A) 94 feet by 25 feet
B) 82 feet by 26 feet
C) 85 feet by 25 feet
D) 76 feet by 22 feet
E) 76 feet by 28 feet
times the width. Find the length and width of the tennis court. A) 94 feet by 25 feet
B) 82 feet by 26 feet
C) 85 feet by 25 feet
D) 76 feet by 22 feet
E) 76 feet by 28 feet
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32
Simplify:
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33
Use a graphing calculator to solve the equation. If an answer is not exact, give the result to the nearest hundredth.
A)
B)
C)
D)
A)
B)
C)
D)
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k this deck
34
Graph the equation .
A)
B)
C)
D)
.A)
B)
C)
D)
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k this deck
35
The area of a rectangular region is 187 square feet. If the length and width are each increased by 5 feet, the area is increased by 165 square feet. Find the length and width of the original rectangle.
A) 13 feet by 19 feet
B) 11 feet by 17 feet
C) 10 feet by 16 feet
D) 8 feet by 14 feet
E) 12 feet by 18 feet
A) 13 feet by 19 feet
B) 11 feet by 17 feet
C) 10 feet by 16 feet
D) 8 feet by 14 feet
E) 12 feet by 18 feet
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36
Find the vertex of the graph of the equation. Do not draw the graph.
A)
B)
C)
D)
A)
B)
C)
D)
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37
Graph the parabola and give the coordinates of the vertex.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Write in terms of i and simplify.
A)
B)
C)
D)
E)
in terms of i and simplify.A)
B)
C)
D)
E)
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k this deck
39
Construct a table of solutions and graph of .
A)
B)
C)
D)
.A)
B)
C)
D)
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40
Determine the vertex and axis of symmetry for .
A) vertex: ; axis:
B) vertex: ; axis:
C) vertex: ; axis:
D) vertex: ; axis:
.A) vertex:
; axis: B) vertex:
; axis: C) vertex:
; axis: D) vertex:
; axis: Unlock Deck
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41
Write the expression in form.
A)
B)
C)
D)
E)
form. A)
B)
C)
D)
E)
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42
Solve the following quadratic equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
43
Write in terms of i and simplify.
A)
B)
C)
D)
E)
in terms of i and simplify.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
44
Solve the following quadratic equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
45
Perform the operation. Write the answer in a + bi form.
A)
B)
C)
D)
A)
B)
C)
D)
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Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
46
Write the expression in a + bi form.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
47
Write in terms of i , perform the indicated operations, and simplify.
A)
B)
C)
D)
E)
in terms of i , perform the indicated operations, and simplify.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
48
Write the expression in a + bi form.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
49
Simplify the expression. Enter the answer in a + bi form.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
50
Simplify the expression. Enter the answer in a + bi form.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
51
Solve the equation. Enter all roots in bi or a + bi form.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 51 flashcards in this deck.
