AnswersFL-1200710-Mathematics for College Algebra AAdding and Subtracting Polynomials

Quadratic Functions: Factored Form Answers

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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.
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.
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.

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