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

Quadratic Functions: Standard Form Answers

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The a value of a function in the form f(x) = ax2 + bx + c is negative. Which statement must be true?

A
The vertex is a maximum.
B
The y-intercept is negative.
C
The x-intercepts are negative.
D
The axis of symmetry is to the left of zero.
2
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Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Select two options.

A
The domain of the function is .
Option A
B
The range of the function is all real numbers.
C
The vertex of the function is .
Option C
D
The function has two x-intercepts.
E
The function is increasing over the interval (, ∞).
Option E
3

The graph of which function has an axis of symmetry at x = 3?

A
f(x) = x2 + 3x + 1
Option A
B
f(x) = x2 – 3x – 3
Option B
C
f(x) = x2 + 6x + 3
Option C
D
f(x) = x2 – 6x – 1
Option D
4

On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 2), has a vertex at (1.5, 10), and goes through (5, negative 2).

Question illustration
A
(–∞, 1.5)
B
(–∞, 10.25)
C
(1.5, ∞)
D
(10.25, ∞)
5

The axis of symmetry for the graph of the function is x=6. What is the value of b?

Question illustration
A
−12
B
−3
C
Option
Option C
D
3
6

What is the y-intercept of the graph of the function f(x) = x2 + 3x + 5?

A
(0, –5)
B
(0, –3)
C
(0, 3)
D
(0, 5)
7

On a coordinate plane, a parabola opens up. It goes through (negative 8, negative 2), has a vertex at (negative 5, negative 6.5), goes through (negative 2, negative 2), and has a y-intercept at (0, 6).

Question illustration
A
(–6.5, ∞)
B
(–5, ∞)
C
(–∞, –5)
D
(–∞, –6.5)
8

The axis of symmetry for the graph of the function f(x)=3x2+bx+4 is . What is the value of b?

Question illustration
A
−18
B
−9
C
9
D
18
9

The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?

A
(−5, 41)
B
(−5, 56)
C
(−5, 76)
D
(−5, 91)
10

Tempestt graphs a function that has a maximum located at (–4, 2). Which could be her graph?

A
On a coordinate plane, a parabola opens up. It goes through (negative 6, 6), has a vertex at (negative 4, 2), and goes through (negative 2, 6).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (2, 6), has a vertex at (4, 2), and goes through (6, 6).
Option B
C
On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 2), has a vertex at (negative 4, 2), and goes through (negative 2, negative 2).
Option C
D
On a coordinate plane, a parabola opens down. It goes through (2, negative 2), has a vertex at (4, 2), and goes through (6, negative 2).
Option D

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