AnswersAISD Algebra I-B Credit Recovery 2026-2027Transformations of Quadratic Functions

Transformations of Quadratic Functions — Unit test Answers

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1
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The height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 – 5t2, where t is the time in seconds. A high-speed camera is ready to film the person between 15 m and 10 m above the ground. For which interval of time should the camera film the person?

A
Option
B
✓ Correct
C
Option
D
t < 2
2
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Gabe is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by a parabola that opens upward with a diameter of 4 in. and a depth of 1 in. The vertex of the parabola is at the origin. Where should Gabe place the bulb to ensure a perfect beam of light?

A
(0, 1)
B
(0, 4)
C
(1, 0)
D
(4, 0)
3

What is the solution set of the quadratic inequality

Question illustration
A
Option
B
Option
C
Option
D
✓ Correct
4

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by , where x and y are measured in inches. Where is the focus of the flashlight?

Question illustration
A
(–2, –0.5)
B
(2, –5.5)
C
(2, 5.5)
D
(5.5, 2)
5

A rectangular pan has a length that is the width. The total area of the pan is 432 in.2. What is the width of the cake pan?A = lw

Question illustration
A
10.4 in.
B
13.9 in.
C
18 in. ✓ Correct
D
24 in.
6

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? V = lwhP = 2(l + w)

A
y = 5(28 – x)(x)
B
y = 5(28 – 2x)(x)
C
y = 5(14 – x)(x)
D
y = 5(14 – 2x)(x)
7

Aramis is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by , where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. Where should the feed antenna be placed?

Question illustration
A
0.75 in. below the vertex
B
0.75 in. to the right of the vertex
C
0.75 in. to the left of the vertex
D
0.75 in. above the vertex ✓ Correct
8

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?

A
Option
B
✓ Correct
C
Option
D
Option
9

When a baseball is hit by a batter, the height of the ball, h(t), at time t, , is determined by the equation . If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

Question illustration
A
mc018-3.jpg
Option A
B
mc018-4.jpg
Option B
C
mc018-5.jpg
Option C
D
mc018-6.jpg
Option D
10

When a baseball is hit by a batter, the height of the ball, h(t), at time t, , is determined by the equation . If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

Question illustration
A
mc018-3.jpg
Option A
B
mc018-4.jpg
Option B
C
mc018-5.jpg
Option C
D
mc018-6.jpg
Option D
11

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? V = lwhP = 2(l + w)

A
y = 5(28 – x)(x)
B
y = 5(28 – 2x)(x)
C
y = 5(14 – x)(x)
D
y = 5(14 – 2x)(x)
12

What is the distance from the origin to point P graphed on the complex plane below?

Question illustration
A
StartRoot 7 EndRoot
Option A
B
StartRoot 29 EndRoot
Option B
C
7
D
29
13

A rectangular pan has a length that is the width. The total area of the pan is 432 in.2. What is the width of the cake pan?A = lw

Question illustration
A
10.4 in.
B
13.9 in.
C
18 in.
D
24 in.
14

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

A
m greater-than StartFraction 25 Over 3 EndFraction
Option A
B
m less-than StartFraction 25 Over 3 EndFraction
Option B
C
m less-than StartFraction 49 Over 12 EndFraction
Option C
D
m greater-than StartFraction 49 Over 12 EndFraction
Option D
15

In which quadrant is the number 6 – 8i located on the complex plane?

A
I
B
II
C
III
D
IV
16

Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?

A
y = 9 (x + one-half) squared minus thirteen-fourths
Option A
B
y = 9 (x + one-half) squared minus 1
Option B
C
y = 9 (x + one-half) squared + five-fourths
Option C
D
y = 9 (x + one-half) squared minus five-fourths
Option D
17

Which statement about the following equation is true?2x2 – 9x + 2 = –1

A
The discriminant is less than 0, so there are two real roots.
B
The discriminant is less than 0, so there are two complex roots.
C
The discriminant is greater than 0, so there are two real roots.
D
The discriminant is greater than 0, so there are two complex roots.
18

Solve for in the equation .

Question illustration
A
x = negative 4 plus-or-minus StartRoot 37 EndRoot i
Option A
B
x = –4 ± 5i
C
x = 4 plus-or-minus StartRoot 37 EndRoot i
Option C
D
x = 4 ± 5i
19

A projectile is fired straight up from ground level with an initial velocity of 112 ft/s. Its height, h, above the ground after t seconds is given by h = –16t2 + 112t. What is the interval of time during which the projectile's height exceeds 192 feet?

A
3 < t < 4
B
t < 4
C
t > 4
D
3 > t > 4
20

The graph below shows the height of a projectile t seconds after it is launched. If acceleration due to gravity is –16 ft/s2, which equation models the height of the projectile correctly?h(t) = at2 + vt + h0

Question illustration
A
h(t) = –16t2 + 42t + 5
B
h(t) = –16t2 + 5
C
h(t) = –16t2 + 32
D
h(t) = –16t2 + 32t + 5

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