AnswersInt Math II Sem 1 2025-2026Unit 2 Test

Unit 2 Test Answers

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1
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Mischa wrote the quadratic equation 0=-x2+4x-7 in standard form. If a = -1, what is the value of c in her equation?

A
c=-7
B
c=-1
C
c=4
D
c=7
2
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What are the solutions to the quadratic equation 4(x + 2)2 = 36

A
x = −11 and x = 7
B
x = −7 and x = 11
C
x = −5 and x = 1
D
x = −1 and x = 5
3

Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo.

A
8 inches by 8 inches
B
9 inches by 9 inches
C
12 inches by 12 inches
D
13 inches by 13 inches
4

The first two steps in determining the solution set of the system of equations, y = –x2 + 4x + 12 and y = –3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations?

Question illustration
A
(3, 15)
B
(–4, 36)
C
(3, 15) and (4, 12)
D
(–3, 33) and (–4, 36)
5

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

Question illustration
A
{–7, 1}
B
(negative 3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)
C
(3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)
D
{1, 7}
6

The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)?

A
g(x) = (x – 2)2 + k
B
g(x) = (x + 8)2 + k
C
g(x) = (x – h)2 – 5
D
g(x) = (x – h)2 – 15
7

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has?

A
The discriminant is −55, so the equation has 2 real solutions.
B
The discriminant is −55, so the equation has no real solutions.
C
The discriminant is 73, so the equation has 2 real solutions.
D
The discriminant is 73, so the equation has no real solutions.
8

Which equation has an a-value of –2, a b-value of 1, and a c-value of 3?

A
0 = –2x2 + x + 3
B
0 = 2x2 + x + 3
C
0 = –2x2 + 3
D
0 = 2x2 – x + 3
9

Adam is using the equation (x)(x + 2) = 255 to find two consecutive odd integers with a product of 255. When Adam solves the problem using the zero product property, what do those solutions represent?

A
two possible “first” integers
B
two possible “second” integers
C
the two consecutive odd integers with a product of 255
D
a possible “first” integer and a possible “second” integer
10

Use the zero product property to find the solutions to the equation x2 – 9 = 16.

A
x = –3 or x = 3
B
x = –6 or x = –3
C
x = –5 or x = 5
D
x = 7 or x = 1
11

Which is the graph of a quadratic equation that has a negative discriminant?

A
On a coordinate plane, a parabola opens down. It goes through (negative 4, negative 4), has a vertex at (negative 2, 0), and goes through (0, negative 4).
Option A
B
On a coordinate plane, a parabola opens down. It goes through (negative 4, negative 4), has a vertex at (negative 2, 0), and goes through (0, negative 4).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 4, 4), has a vertex at (negative 2, 0), and goes through (0, 4).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 4, 8), has a vertex at (negative 2, 4), and goes through (0, 8).
Option D
12

The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form.

Question illustration
A
f(x) = (x + 2)2 + 3
B
f(x) = (x2 + 2x)2 + 3
C
f(x) = (x + 1)2 + 2
D
f(x) = (x + 3)2 + 2x
13

Use the zero product property to find the solutions to the equation 2x2 + x – 1 = 2.

A
x = or x = 2
Option A
B
x = –2 or x =
Option B
C
x = or x = 1
Option C
D
x = 1 or x =
Option D
14

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

A
right 5, down 23
B
left 5, down 23
C
right 5, up 27
D
left 5, up 27
15

The product of two consecutive integers is 272. Which quadratic equation can be used to find x, the smaller number?

A
x2 + 1 = 272
B
x2 − 1 = 272
C
x2 + x − 272 = 0
D
x2 + x + 272 = 0

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