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

Transformations of Quadratic Functions Answers

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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?

h and k cannot both equal zero

k and c have the same value

the value of a remains the same

h is equal to one half –b

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What is the first step when rewriting y = 3x2 + 9x – 18 in the form y = a(x – h)2 + k?

3 must be factored from 3x2 + 9x

x must be factored from 3x2 + 9x

9 must be factored from 9x – 18

3 must be factored from 3x2 – 18

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

y = 2(x – 2)2 + 9

y = 2(x – 2)2 + 5

y = 2(x – 2)2 + 1

y = 2(x – 2)2 + 17

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

16 must be factored from 18x + 14

x must be factored from 6x2 + 18x

6 must be factored from 6x2 + 14

6 must be factored from 6x2 + 18x

Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3?

4 units to the left

4 units to the right

8 units to the left

8 units to the right

Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x + 1)2?

6 unit left

6 unit right

1 unit left

1 unit right

Which pair of equations generates graphs with the same vertex?

y = –(x + 4)2 and y = (x – 4)2

y = –4x2 and y = 4x2

y = –x2 – 4 and y = x2 + 4

y = (x – 4)2 and y = x2 + 4

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

y = (x – 1)2 + 1

y = (x – 1)2 – 1

y = (x + 1)2 + 1

y = (x + 1)2 – 1

Which equation is y = 6x2 + 12x – 10 rewritten in vertex form?

y = 6(x + 1)2 – 11

y = 6(x + 1)2 – 10

y = 6(x + 1)2 – 4

y = 6(x + 1)2 – 16

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

y = 2 (x + seven-halves) squared minus one-fourth

y = 2 (x + seven-halves) squared minus one-half

y = 2(x + 7)2 – 73

y = (x + 7)2 – 24

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Transformations of Quadratic Functions Answers

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