AnswersAZ-Common Core Algebra II ASquare Root Functions

Square Root Functions — Unit test Answers

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During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?

A
the height of the bird and the ball when the ball and the bird are the same distance from the player
B
the height of the bird and the ball when the player hits the ball
C
the time when the height of the ball and the bird are the same
D
the time when the ball and the bird hit the ground
2
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Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

What is the value of i 97 – i?

A
–i
B
0
C
–2i
D
i Superscript 96
Option D
4

Which expression is equivalent to (4 + 6i)2?

A
–20 + 48i
B
8 + 12i
C
16 – 36i
D
20 + 48i
5

If , which inequality can be used to find the domain of f(x)?

Question illustration
A
StartRoot 4 x EndRoot greater-than-or-equal-to 0
Option A
B
4 x + 9 greater-than-or-equal-to 0
Option B
C
4 x greater-than-or-equal-to 0
Option C
D
StartRoot 4 x + 9 EndRoot + 2 greater-than-or-equal-to 0
Option D
6

Which pair of complex numbers has a real-number product?

A
(1 + 3i)(6i)
B
(1 + 3i)(2 – 3i)
C
(1 + 3i)(1 – 3i)
D
(1 + 3i)(3i)
7

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

A
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction
Option A
B
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction
Option B
C
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction
Option C
D
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction
Option D
8

Which equation represents a graph with a vertex at (1, –6)?

A
y = 3x2 + 6x – 3
B
y = 3x2 – 6x – 3
C
y = 3x2 – 8x – 1
D
y = 3x2 – 3x – 6
9

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

Which system is equivalent to

Question illustration
A
StartLayout Enlarged left-brace 1st row 5 minus x = 9 x squared 2nd row y = 5 minus x EndLayout
Option A
B
StartLayout Enlarged left-brace 1st row y = 9 y squared minus 90 y + 225 2nd row x = y minus 5 EndLayout
Option B
C
StartLayout Enlarged left-brace 1st row 5 + x = 9 x squared 2nd row y = 5 + x EndLayout
Option C
D
StartLayout Enlarged left-brace 1st row y = 3 x 2nd row x + 3 x = 5 EndLayout
Option D
11

Which equation is the inverse of y = x2 – 36?

A
y = plus-or-minus StartRoot x EndRoot + 6
Option A
B
y = plus-or-minus StartRoot x + 36 EndRoot
Option B
C
y = plus-or-minus StartRoot x EndRoot + 36
Option C
D
y = plus-or-minus StartRoot x squared + 36 EndRoot
Option D
12

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

A
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction
Option A
B
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction
Option B
C
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction
Option C
D
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction
Option D
13

Which point shows the location of 5 – 2i on the complex plane below?

Question illustration
A
point A
B
point B
C
point C
D
point D
14

During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y = –0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation y = –0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

A
the height at which the pumpkins reach their greatest horizontal distance from the launch site
B
the horizontal distance of the pumpkins from the launch site when they reach the ground
C
the starting height of the pumpkins when they are at the launch site
D
the horizontal distance of the pumpkins from the launch site when their heights are the same
15

If , which inequality can be used to find the domain of f(x)?

Question illustration
A
StartRoot 4 x EndRoot greater-than-or-equal-to 0
Option A
B
4 x + 9 greater-than-or-equal-to 0
Option B
C
4 x greater-than-or-equal-to 0
Option C
D
StartRoot 4 x + 9 EndRoot + 2 greater-than-or-equal-to 0
Option D
16

Solve for in the equation .

Question illustration
A
x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
Option A
B
x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
Option B
C
x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option C
D
x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option D
17

Dimitri is solving the equation x2 – 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

A
0
B
4
C
25
D
100
18

What is one solution of the following system?

Question illustration
A
(–6, 0)
B
(–2, 4)
C
(0, –6)
D
(4, –2)
19

During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?

A
the height of the bird and the ball when the ball and the bird are the same distance from the player
B
the height of the bird and the ball when the player hits the ball
C
the time when the height of the ball and the bird are the same
D
the time when the ball and the bird hit the ground
20

If the discriminant of a quadratic equation is 4, which statement describes the roots?

A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.

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