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

A
I
B
II
C
III
D
IV
2
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What is the absolute value of the complex number ?

Question illustration
A
StartRoot 14 EndRoot
Option A
B
3 StartRoot 2 EndRoot
Option B
C
14
D
18
3

Use completing the square to solve for in the equation .

Question illustration
A
x = –1 or 15
B
x = 1 or 7
C
x = 4 plus-or-minus StartRoot 41 EndRoot
Option C
D
x = 4 plus-or-minus StartRoot 73 EndRoot
Option D
4

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 + i) + (21 + 5i)?

A
(–1 + i) + (21 + 5i) + 0
B
–1 + (i + 21) + 5i
C
(–1 + 21) + (i + 5i)
D
–(1 – i) + (21 + 5i)
5

Which equation has a graph that lies entirely above the x-axis?

A
y = –(x + 7)2 + 7
B
y = (x – 7)2 – 7
C
y = (x – 7)2 + 7
D
y = (x – 7)2
6

Solve for in the equation .

Question illustration
A
x = 6 plus-or-minus 3 StartRoot 10 EndRoot
Option A
B
x = 6 plus-or-minus 2 StartRoot 7 EndRoot
Option B
C
x = 12 plus-or-minus 3 StartRoot 22 EndRoot
Option C
D
x = 12 plus-or-minus 3 StartRoot 10 EndRoot
Option D
7

Which equation represents a graph with a vertex at (–3, 2)?

A
y = 4x2 + 24x + 38
B
y = 4x2 – 24x + 38
C
y = 4x2 + 12x + 2
D
y = 4x2 + 16x + 13
8

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.
9

Using the quadratic formula to solve 4x2 – 3x + 9 = 2x + 1, what are the values of x?

A
StartRoot 1 plus-or-minus StartRoot 159 EndRoot i Over 8 EndFraction
Option A
B
StartRoot 5 plus-or-minus StartRoot 153 EndRoot i Over 8 EndFraction
Option B
C
StartRoot 5 plus-or-minus StartRoot 103 EndRoot i Over 8 EndFraction
Option C
D
StartRoot 1 plus-or-minus StartRoot 153 EndRoot Over 8 EndFraction
Option D
10

Which values of x and y would make the following expression represent a real number?(4 + 5i)(x + yi)

A
x = 4, y = 5
B
x = –4, y = 0
C
x = 4, y = –5
D
x = 0, y = 5
11

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
12

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
13

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

A
1
B
–1
C
i
D
–i
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

Which equation demonstrates the multiplicative identity property?

A
(negative 3 + 5 i) + 0 = negative 3 + 5 i
Option A
B
(negative 3 + 5 i ) (1) = negative 3 + 5 i
Option B
C
(negative 3 + 5 i) (negative 3 + 5 i) = negative 16 minus 30 i
Option C
D
(negative 3 + 5 i) (3 minus 5 i) = 16 + 30 i
Option D
16

Which statement about the following equation is true?3x2 – 8x + 5 = 5x2

A
The discriminant is less than 0, so there are two real roots.
B
The discriminant is greater than 0, so there are two real roots.
C
The discriminant is less than 0, so there are two complex roots.
D
The discriminant is greater than 0, so there are two complex roots.
17

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
18

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

A
x2 + mx + m = (x – 1)2
B
x2 + mx + m = (x + 1)2
C
x2 + mx + m = (x + 2)2
D
x2 + mx + m = (x + 4)2
19

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?

A
The complex numbers have equal imaginary parts.
B
The complex numbers have equal real parts.
C
The complex numbers have opposite imaginary parts.
D
The complex numbers have opposite real parts.
20

Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?

A
6 units left and 9 units down
B
6 units right and 9 units down
C
6 units left and 9 units up
D
6 units right and 9 units up

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