AnswersAlgebra III AQuadratic Functions: Vertex Form

Quadratic Functions: Vertex Form Answers

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The graph shows the axis of symmetry for a quadratic function f(x).

Question illustration
A
f(x) = (x + 4)2
B
f(x) = x2 + 4
C
f(x) = (x – 4)2
D
f(x) = x2 – 4
2
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Which function has a range of {y|y ≤ 5}?

A
f(x) = (x – 4)2 + 5
B
f(x) = –(x – 4)2 + 5
C
f(x) = (x – 5)2 + 4
D
f(x) = –(x – 5)2 + 4
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 (0, 7), has a vertex at (2, 3), and goes through (4, 7).

Question illustration
A
right 2, up 3
B
left 2, down 3
C
right 2, down 3
D
left 2, up 3
4

Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasing?

A
(negative 8, infinity)
Option A
B
(8, infinity)
Option B
C
(negative infinity, 8)
Option C
D
(negative infinity, negative 8)
Option D
5

The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)?

A
g(x) = (x + 9)2 + 4
B
g(x) = (x + 9)2 − 4
C
g(x) = (x − 4)2 + 9
D
g(x) = (x + 4)2 + 9
6

Which graph represents the function f(x) = (x – 5)2 + 3?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?

A
On a coordinate plane, a vertical dashed line at (negative 2, 0) is parallel to the y-axis.
Option A
B
On a coordinate plane, a vertical dashed line at (2, 0) is parallel to the y-axis.
Option B
C
On a coordinate plane, a vertical dashed line at (negative 1, 0) is parallel to the y-axis.
Option C
D
On a coordinate plane, a vertical dashed line at (1, 0) is parallel to the y-axis.
Option D
8

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.Which graph represents g(x)?

Question illustration
A
On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
Option D
9

What value represents the horizontal translation from the graph of the parent function f(x) = x2 to the graph of the function g(x)=(x−4)2+2?

A
−4
B
−2
C
2
D
4
10

The graph of which function is decreasing over the interval (–4, ∞)?

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

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