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Quadratic Functions: Vertex Form Answers

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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 (negative 6, 10), has a vertex at (negative 4, 6), and goes through (negative 2, 10).

Question illustration
A
g(x) = (x – 4)2 + 6
B
g(x) = (x + 6)2 – 4
C
g(x) = (x – 6)2 – 4
D
g(x) = (x + 4)2 + 6
2
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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
3

The graph of g(x) is a translation of the function f(x) = x2. The vertex of g(x) is located 5 units above and 7 units to the right of the vertex of f(x). Which equation represents g(x)?

A
g(x) = (x + 7)2 + 5
B
g(x) = (x – 7)2 + 5
C
g(x) = (x + 5)2 + 7
D
g(x) = (x – 5)2 + 7
4

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
5

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
6

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 (negative 5, 8), has a vertex at (negative 3, 4), and goes through (negative 1, 8).

Question illustration
A
left 3, up 4
B
right 3, down 4
C
left 3, down 4
D
right 3, up 4
7

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
8

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
9

Sanjay begins to correctly graph the function f(x) = (x + 1)2 – 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay’s?

A
On a coordinate plane, a vertical dashed line at (1, 0) is parallel to the y-axis. A solid circle appears on the dashed line at (1, negative 3).
Option A
B
On a coordinate plane, a vertical dashed line at (negative 3, 0) is parallel to the y-axis. A solid circle appears on the dashed line at (negative 3, 1).
Option B
C
On a coordinate plane, a vertical dashed line at (negative 1, 0) is parallel to the y-axis. A solid circle appears on the dashed line at (negative 1, negative 3).
Option C
D
On a coordinate plane, a vertical dashed line at (3, 0) is parallel to the y-axis. A solid circle appears on the dashed line at (3, negative 1).
Option D
10

What value represents the vertical translation from the graph of the parent function f(x)=x2 to the graph of the function g(x)=(x+5)2+3?

A
−5
B
−3
C
3
D
5
11

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
12

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
13

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
14

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
15

The graph of f(x) = x2 is translated to formg(x) = (x – 2)2 – 3.Which graph represents g(x)?

Question illustration
A
On a coordinate plane, a parabola opens up. It goes through (0, 1), has a vertex at (2, negative 3), and goes through (4, 1).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 3, 4), has a vertex at (negative 2, 3), and goes through (negative 1, 4).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (1, 4), has a vertex at (2, 3), and goes through (3, 4).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 4, 1), has a vertex at (negative 2, negative 3), and goes through (0, 1).
Option D

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