AnswersCSD Summer 2026 Algebra 1Unit Test

Unit Test — Unit test Answers

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1
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Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6?

A
left 1 unit, up 5 units
B
right 1 unit, up 5 units
C
left 2 units, up 2 units
D
right 2 units, up 2 units
2
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What is the axis of symmetry for the function f(x)=7−4x+x2?

A
x = –3
B
x = –2
C
x = 2
D
x = 3
3

On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (3, 6), has a vertex at (5, 2), and goes through (7, 6).

Question illustration
A
g(x) = (x + 5)2 + 2
B
g(x) = (x + 2)2 + 5
C
g(x) = (x – 2)2 + 5
D
g(x) = (x – 5)2 + 2
4

According to one company’s profit model, the company has a profit of 0 when 10 units are sold and a maximum profit of $18,050 when 105 units are sold. What is the function that represents this company’s profit f(x) depending on the number of items sold, x?

A
f(x)=−2(x+105)2+18,050
B
f(x)=−2(x−105)2+18,050
C
f(x)=−10(x+105)2+18,050
D
f(x)=−10(x−105)2+18,050
5

A 2-column table with 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 3, negative 2, negative 3, 0, 7.

Question illustration
A
one-fifth
Option A
B
4
C
5
D
10
6

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.Write the function in standard form.f(x) = 5x2 + 40xFactor a out of the first two terms.f(x) = 5(x2 + 8x)Form a perfect square trinomial. = 16 f(x) = 5(x2 + 8x + 16) – 5(16)What is the function written in vertex form?

Question illustration
A
f(x) = 5(x + 4) – 80
B
f(x) = 5(x + 8) – 80
C
f(x) = 5(x + 4)2 – 80
D
f(x) = 5(x + 8)2 – 80
7

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.f(x) = 4(x2 + 12x) + 10 = 36

Question illustration
A
f(x) = 4(x + 6)2 + 10
B
f(x) = 4(x + 6)2 – 26
C
f(x) = 4(x + 6)2 – 134
D
f(x) = 4(x + 6)2 + 154
8

The function f(x) = −(x + 5)(x + 1) is shown.

Question illustration
A
all real numbers less than or equal to 4
B
all real numbers less than or equal to −3
C
all real numbers greater than or equal to 4
D
all real numbers greater than or equal to −3
9

Mary throws a plastic disc to her friend. Her friend catches the disc six seconds after Mary throws it. The table shows the height of the disc at one-second intervals.

Question illustration
A
A = 5, B = 3
B
A = 4, B = 0
C
A = 4, B = 3
D
A = 5, B = 0
10

The function f(x) = –(x – 3)2 + 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

A
3 square units
B
6 square units
C
9 square units
D
12 square units
11

On a coordinate plane, a parabola opens up. It starts in quadrant 1, crosses the x axis where the vertex is in quadrant 4, and crosses the x-axis back into quadrant 1.

Question illustration
A
f(x) = (x – 8)2 + 6
B
f(x) = (x + 8)2 + 6
C
f(x) = (x + 8)2 – 6
D
f(x) = (x – 8)2 – 6
12

Which point is an x-intercept of the quadratic functionf(x) = (x – 8)(x + 9)?

A
(0,8)
B
(0,–8)
C
(9,0)
D
(–9,0)
13

On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).

Question illustration
A
The domain is all real numbers. The range is {y|y < 16}.
B
The domain is all real numbers. The range is {y|y ≤ 16}.
C
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
D
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.
14

Consider the function shown on the graph.

Question illustration
A
f(x) = (x + 3)(x + 7)
B
f(x) = (x – 3)(x – 7)
C
f(x) = 3(x – 3)(x – 7)
D
f(x) = 11(x + 3)(x + 7)
15

Which function has an axis of symmetry of x = −2?

A
f(x) = (x − 1)2 + 2
B
f(x) = (x + 1)2 − 2
C
f(x) = (x − 2)2 − 1
D
f(x) = (x + 2)2 − 1
16

Given the function f(x) = −5x2 − x + 20, find f(3).

A
−28
B
−13
C
62
D
64
17

What is the vertex of the graph of the function f(x) = x2 + 8x − 2 ?

A
(−4, 18)
B
(0, -2)
C
(-8, -2)
D
(−4, −18)
18

Which quadratic function is the standard form of the equation shown?f(x) = x + 8 + 2x + 5x2

A
f(x) = 8 + 5x2 + 2x + x
B
f(x) = x + 2x + 5x2 + 8
C
f(x) = 8 + 3x + 5x2
D
f(x) = 5x2 + 3x + 8
19

What are the x-intercepts of the function f(x) = –x2 – x + 2?

A
(–2, 0) and (1, 0)
B
(2, 0) and (1, 0)
C
(–2, 0) and (-1, 0)
D
(0, -2) and (0, 1)
20

Which is one of the transformations applied to the graph of f(x)=x2 to change it into the graph of g(x) = –x2 + 16x – 44?

A
The graph of f(x) = x2 is widened.
B
The graph of f(x) = x2 is shifted left 8 units.
C
The graph of f(x) = x2 is shifted down 44 units.
D
The graph of f(x) = x2 is reflected over the x-axis.

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