AnswersAISD Algebra I-B Credit Recovery 2026-2027Transformations of Quadratic Functions

Transformations of Quadratic Functions Answers

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Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?

A
y = 2 (x + seven-halves) squared minus one-fourth
Option A
B
y = 2 (x + seven-halves) squared minus one-half
Option B
C
y = 2(x + 7)2 – 73
D
y = (x + 7)2 – 24
2
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What is the first step when rewriting y = –4x2 + 2x – 7 in the form y = a(x – h)2 + k?

A
2 must be factored from 2x – 7
B
–4 must be factored from –4x2 + 2x
C
x must be factored from –4x2 + 2x
D
–4 must be factored from –4x2 – 7
3

Which equation is y = 2x2 – 8x + 9 rewritten in vertex form?

A
y = 2(x – 2)2 + 9
B
y = 2(x – 2)2 + 5
C
y = 2(x – 2)2 + 1
D
y = 2(x – 2)2 + 17
4

Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x – h)2 + k. Which of the following must be true?

A
h and k cannot both equal zero
B
k and c have the same value
C
the value of a remains the same
D
h is equal to one half –b
5

Which equation has a graph that is a parabola with a vertex at (5, 3)?

A
y = (x – 5)2 + 3
B
y = (x + 5)2 + 3
C
y = (x – 3)2 + 5
D
y = (x + 3)2 + 5
6

What is the first step when rewriting y = 6x2 + 18x + 14 in the form y = a(x – h)2 + k?

A
16 must be factored from 18x + 14
B
x must be factored from 6x2 + 18x
C
6 must be factored from 6x2 + 14
D
6 must be factored from 6x2 + 18x
7

Which equation has a graph that is a parabola with a vertex at (–1, –1)?

A
y = (x – 1)2 + 1
B
y = (x – 1)2 – 1
C
y = (x + 1)2 + 1
D
y = (x + 1)2 – 1
8

Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?

A
y = 2 (x + seven-halves) squared minus one-fourth
Option A
B
y = 2 (x + seven-halves) squared minus one-half
Option B
C
y = 2(x + 7)2 – 73
D
y = (x + 7)2 – 24
9

How does the graph of y = a(x – h)2 + k change if the value of h is doubled?

A
The vertex of the graph moves to a point twice as far from the x-axis.
B
The vertex of the graph moves to a point twice as far from the y-axis.
C
The vertex of the graph moves to a point half as far from the x-axis.
D
The vertex of the graph moves to a point half as far from the y-axis.
10

Which pair of equations generates graphs with the same vertex?

A
y = –(x + 4)2 and y = (x – 4)2
B
y = –4x2 and y = 4x2
C
y = –x2 – 4 and y = x2 + 4
D
y = (x – 4)2 and y = x2 + 4

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