AnswersFL-1200700-Mathematics for College Algebra MISAdding and Subtracting Polynomials

Quadratic Functions: Factored Form Answers

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1
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What is the y-intercept of the quadratic functionf(x) = (x – 8)(x + 3)?

A
(8,0)
B
(0,3)
C
(0,–24)
D
(–5,0)
2
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The graph of the function f(x) = –(x + 6)(x + 2) is shown below.

Question illustration
A
The function is increasing for all real values of x where x < –4.
B
The function is increasing for all real values of x where–6 < x < –2.
C
The function is decreasing for all real values of x where x –2.
D
The function is decreasing for all real values of x wherex < –4.
3

What is the equation of the quadratic function with a vertex at (2,–25) and an x-intercept at (7,0)?

A
f(x) = (x – 2)(x – 7)
B
f(x) = (x + 2)(x + 7)
C
f(x) = (x – 3)(x + 7)
D
f(x) = (x + 3)(x – 7)
4

Which statements about the function are true? Select two options.

A
The vertex of the function is at (1,–25).
B
The vertex of the function is at (1,–24).
C
The graph is increasing only on the interval −4< x < 6.
D
The graph is positive only on one interval, where x < –4.
E
The graph is negative on the entire interval–4 < x < 6.
5

Which is the graph of f(x) = –(x + 3)(x + 1)?

A
Option
B
Option
C
Option
D
Option
6

What is the y-intercept of the quadratic functionf(x) = (x – 6)(x – 2)?

A
(0,–6)
B
(0,12)
C
(–8,0)
D
(2,0)
7

Which function has two x-intercepts, one at (0, 0) and one at (4, 0)?

A
f(x) = x(x − 4)
B
f(x) = x(x + 4)
C
f(x) = (x − 4)(x − 4)
D
f(x) = (x + 4)(x + 4)
8

The graph of the function f(x) = (x – 4)(x + 1) is shown below.

Question illustration
A
The function is increasing for all real values of x wherex < 0.
B
The function is increasing for all real values of x wherex 4.
C
The function is decreasing for all real values of x where–1 < x < 4.
D
The function is decreasing for all real values of x wherex < 1.5.
9

What is the midpoint of the x-intercepts off(x) = (x – 2)(x – 4)?

A
(–3,0)
B
(–1,0)
C
(1,0)
D
(3,0)
10

The graph of the function f(x) = (x +2)(x + 6) is shown below.

Question illustration
A
The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
B
The domain is all real numbers greater than or equal to –4, and the range is all real numbers.
C
The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.
D
The domain is all real numbers greater than or equal to –4, and the range is all real numbers such that –6 ≤ x ≤ –2.
11

What is the equation of the quadratic function with a vertex at (2,–25) and an x-intercept at (7,0)?

A
f(x) = (x – 2)(x – 7)
B
f(x) = (x + 2)(x + 7)
C
f(x) = (x – 3)(x + 7)
D
f(x) = (x + 3)(x – 7)
12

Which is the graph of f(x) = (x – 1)(x + 4)?

A
Option
B
Option
C
Option
D
Option
13

Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?

A
(0,6)
B
(0,–6)
C
(6,0)
D
(–6,0)
14

The graph of the function f(x) = –(x + 6)(x + 2) is shown below.

Question illustration
A
The function is increasing for all real values of x where x < –4.
B
The function is increasing for all real values of x where–6 < x < –2.
C
The function is decreasing for all real values of x where x –2.
D
The function is decreasing for all real values of x wherex < –4.
15

The graph of the function f(x) = (x + 2)(x + 6) is shown below.

Question illustration
A
The function is positive for all real values of x wherex > –4.
B
The function is negative for all real values of x where–6 < x < –2.
C
The function is positive for all real values of x wherex –3.
D
The function is negative for all real values of x wherex < –2.
16

Which function has a vertex at the origin?

A
f(x) = (x + 4)2
B
f(x) = x(x – 4)
C
f(x) = (x – 4)(x + 4)
D
f(x) = –x2
17

What is the axis of symmetry of the function f(x)=−(x+9)(x−21)?

A
x=−15
B
x=−6
C
x=6
D
x=15
18

The function f(x) = (x − 4)(x − 2) is shown.

Question illustration
A
all real numbers less than or equal to 3
B
all real numbers less than or equal to −1
C
all real numbers greater than or equal to 3
D
all real numbers greater than or equal to −1
19

Which function has only one x-intercept at (−6, 0)?

A
f(x) = x(x − 6)
B
f(x) = (x − 6)(x − 6)
C
f(x) = (x + 6)(x − 6)
D
f(x) = (x + 6)(x + 6)
20

The graph of the function f(x) = (x − 3)(x + 1) is shown.

Question illustration
A
all real values of x where x < −1
B
all real values of x where x < 1
C
all real values of x where 1 < x < 3
D
all real values of x where x > 3

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