AnswersCSD Summer 2026 Algebra 1Unit Test

Unit Test — Unit test Answers

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1
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Which equations are true for x = –2 and x = 2? Select two options

A
x2 – 4 = 0
B
x2 = –4
C
3x2 + 12 = 0
D
4x2 = 16
E
2(x – 2)2 = 0
2
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Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?

A
(negative 6 minus StartRoot 51 EndRoot comma negative 6 + StartRoot 51 EndRoot)
Option A
B
(negative 6 minus StartRoot 21 EndRoot comma negative 6 + StartRoot 21 EndRoot)
Option B
C
(6 minus StartRoot 51 EndRoot comma 6 + StartRoot 51 EndRoot)
Option C
D
(6 minus StartRoot 21 EndRoot comma 6 + StartRoot 21 EndRoot)
Option D
3

A rectangle’s length is three times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?

A
w2 = 3(243)
B
3w2 = 243
C
4w2 = 243
D
3w2 = 3(243)
4

What is the first step in solving the quadratic equation -5x2+8=133?

A
taking the square root of both sides of the equation
B
subtracting 8 from both sides of the equation
C
squaring both sides of the equation
D
adding 8 to both sides of the equation
5

Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula below?Quadratic formula: x =

Question illustration
A
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option A
B
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(1) EndRoot Over 2(4) EndFraction
Option B
C
x = StartFraction negative 2 plus or minus StartRoot 2 squared + 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option C
D
x = StartFraction negative 2 plus or minus StartRoot negative 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option D
6

What are the solutions of the quadratic equation (x + 3)2 = 49?

A
x = –2 and x = –16
B
x = 2 and x =
Option B
C
x = 4 and x = –10
D
x = 40 and x = –58
7

A rectangle has an area of 40 square units. The length is 6 units greater than the width.

A
8 by 5
B
10 by 4
C
11 by 9
D
13 by 7
8

What are the solutions to x2 + 8x + 7 = 0?

A
x = –8 and x = –7
B
x = –7 and x = –1
C
x = 1 and x = 7
D
x = 7 and x = 8
9

Isoke is solving the quadratic equation by completing the square.10x2+40x-13=010x2+40x=13A(x2+4x)=13

A
-13
B
4
C
10
D
40
10

Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1?

Question illustration
A
(1, –1)
B
(0, 0) and (0, –1)
C
(0, 0) and (2, 0)
D
no solutions
11

A rectangle’s width is 2 meters shorter than its length, l. Its area is 168 square meters. Which equation can be used to find the length of the rectangle?

A
l(l – 2) = 168
B
l(l + 2) = 168
C
2l 2 = 168
D
l 2 = 168
Option D
12

Which represents the solution(s) of the system of equations, y = x2 – 6x + 8 and y = –x + 4? Determine the solution set by graphing.

A
(1, 3) only
B
(2, 0) and (4, 0)
C
(1, 3) and (4, 0)
D
no solutions
13

Which are the roots of the quadratic function f(q) = q2 – 125? Select two options.

Question illustration
A
q = 5
Option A
B
q = -5
Option B
C
q = 3
Option C
D
q = -3
Option D
E
q = 25
Option E
15

Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?Quadratic formula: x =

Question illustration
A
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
Option A
B
x = StartFraction negative 1 plus or minus StartRoot 1 squared minus 4 (negative 1)(negative 4) EndRoot Over 2(negative 1) EndFraction
Option B
C
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
Option C
D
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 2) EndRoot Over 2(1) EndFraction
Option D
17

Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0=2x2+3x-8?Quadratic formula: x =

Question illustration
A
1.39
B
2.00
C
2.89
D
3.50
18

What are the values of a, b, and c in the quadratic equation 0 = 5x – 4x2 – 2?

A
a = 5, b = 4, c = 2
B
a = 5, b = –4, c = –2
C
a = –4, b = 5, c = –2
D
a = 4, b = –5, c = –2
19

Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. He begins by substituting as shown.Quadratic formula: x = Substitution:

Question illustration
A
The –5 should be 5.
B
The 52 should be –52.
C
The 2 in the numerator should be –2.
D
The 2 in the denominator should be –2.
20

What are the zeros of the quadratic function f(x) = 2x2 – 10x – 3?

A
x = – and x = +
Option A
B
x = – and x = +
Option B
C
x = – and x = +
Option C
D
x = – and x = +
Option D
21

Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?

A
(4 minus StartRoot 19 EndRoot comma 4 + StartRoot 19 EndRoot)
Option A
B
(4 minus StartRoot 11 EndRoot comma 4 + StartRoot 11 EndRoot)
Option B
C
(4 minus StartRoot 8 EndRoot comma 4 + StartRoot 8 EndRoot)
Option C
D
(4 minus StartRoot 3 EndRoot comma 4 + StartRoot 3 EndRoot)
Option D
22

What are the solution(s) of the quadratic equation 98 – x2 = 0?

A
x =
Option A
B
x =
Option B
C
x =
Option C
D
no real solution

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