AnswersEA Academy Algebra IUnit Test

Unit Test — Cumulative exam Answers

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1
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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
2
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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
3

Using the Completing the Square method, what are the zeros of the quadratic function f(x) = 2x2 + 8x – 3?

A
x = –2 – and x = –2 +
Option A
B
x = –2 – and x = –2 +
Option B
C
x = 2 – and x = 2 +
Option C
D
x = 2 – and x = 2 +
Option D
4

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.
5

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
6

Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation?

A
{–22, 14}
B
{–14, 22}
C
{–10, 2}
D
{–2, 10}
7

The curve produced by the water coming from a fountain is sketched on the graph.

Question illustration
A
f(x) = (x – 2)2 + 3
B
f(x) = –(x – 2)2 + 3
C
f(x) = (x + 2)2 + 3
D
f(x) = –(x + 2)2 + 3
8

Clara writes the equation (x – 13)(x + 8) = 196 to solve for the missing side length of a rectangle represented by the factor x + 8. What is the missing side length represented by x + 8 units of the rectangle?

A
7
B
15
C
20
D
28
9

Consider the quadratic function f(x) = x2 – 8x – 4. What is the value of the leading coefficient?

A
–8
B
–4
C
0
D
1
10

Logan saves the same amount of money each month for college. His current total savings is 300m2 + 120m + 180 dollars. Which factorization could represent the number of months and amount of a monthly deposit in dollars?

A
4m(75m2 + 30m +40)
B
10m(30m2 + 12m +18)
C
30(10m2 +4m + 60)
D
60(5m2 +2m +3)
11

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}
12

What are the solutions to m2 – 9 = 0?

m
m = –9 and m = 0
m
m = –3 and m = 3
m
m = –3
m
m = 9
13

The area of a square can be represented by the expression x10. Which monomial represents a side of the square?

A
x2
B
x5
C
x20
D
x100
14

Which expression is equivalent to 64 − 9x2?

A
(32)2 − (3x)2
B
(32)2 + (−3x)2
C
(8)2 − (3x)2
D
(8)2 + (−3x)2
15

Armando used algebra tiles to represent the product .

Question illustration
A
He used the algebra tiles correctly.
B
He did not represent the two original factors correctly.
C
The signs on some of the products are incorrect.
D
Some of the products do not show the correct powers of x.
16

Which equation, when graphed, has x-intercepts at (8, 0) and (−2, 0) and a y-intercept at (0, −48)?

A
f(x) = −3(x − 8)(x + 2)
B
f(x) = −3(x + 8)(x − 2)
C
f(x) = 3(x − 8)(x + 2)
D
f(x) = 3(x + 8)(x − 2)
17

What is the product?(5r − 4)(r2 − 6r + 4)

A
5r3 − 34r2 + 44r − 16
B
5r3 − 4r2 + 14r − 16
C
5r3 − 6r − 16
D
5r3 + 10r − 16
18

Which is the graph of the function f(x) = x2 + 2x + 3?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
19

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
20

A rectangle has an area of (x2 − 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw, what could be the length and width of the rectangle?

A
length = (x − 8) units and width = (x − 9) units
B
length = (x + 9) units and width = (x + 8) units
C
length = (x − 6) units and width = (x − 12) units
D
length = (x + 12) units and width = (x + 6) units

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