Answers26MATH_Recovery_Alg1B22Quadratic Functions: Vertex Form

Quadratic Functions: Vertex Form Answers

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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
2
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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
3

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
4

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
5

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
6

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
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 (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
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

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
10

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

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