Answers26MATH_Recovery_Alg1B22Quadratic Functions: Vertex Form

Completing the Square (Continued) Answers

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1
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What is the first step in writing f(x) = 3x2 + 6x – 8 in vertex form?

A
Factor out 3 from each term.
B
Form a perfect square trinomial by keeping the value of the function equivalent.
C
Write the trinomial as a binomial squared.
D
Factor out 3 from the first two terms.
2
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Write g(x) = 4x2 + 88x in vertex form.

Answers:
=:4(x + 11)^2 - 484
+:4(x + 11)^2 - 484
3

✔ (–3, –45), minimum(–3, 45), maximum(3, –45), minimum(3, 45), maximum

A
✔ (–3, –45), minimum
B
(–3, 45), maximum
C
(3, –45), minimum
D
(3, 45), maximum
4

x = –45✔ x = –3x = 3x = 45

A
x = –45
B
✔ x = –3
C
x = 3
D
x = 45
5

Compare the graphs that Jennifer and Matt drew by completing the statements.

Answers:
Jennifer’s graph is vertically shifted from Matt’s graph.:2 units down
Jennifer’s graph is horizontally shifted from Matt’s graph.:0 units left or right
Jennifer’s graph is Matt’s graph.:the same shape as
Which graph has a vertex that is a maximum?:Neither Jennifer’s nor Matt’s
6

Write p(x) = 21 + 24x + 6x2 in vertex form.

Answers:
p(x) = (x + )2 –:6
p(x) = (x + )2 –:2
p(x) = (x + )2 –:3
7

✔ 241224

A
✔ 2
B
4
C
12
D
24
8

✔ 372124

A
✔ 3
B
7
C
21
D
24
9

What is true about the transformation that was performed? Check all that apply.

A
g(x) has an axis of symmetry at x = 3.
B
g(x) is shifted down 5 units from the graph of f(x).
C
g(x) is shifted right 3 units from the graph of f(x).
D
g(x) is shifted up 4 units from the graph of f(x).
E
g(x) is narrower than f(x).
10

What is h(x) = –3x2 – 6x + 5 written in vertex form?

A
h(x) = –3(x + 1)2 + 2
B
h(x) = –3(x + 1)2 + 8
C
h(x) = –3(x – 3)2 – 4
D
h(x) = –3(x – 3)2 + 32
11

Which functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2? Check all that apply. p(x) = 14(x + 7)2 + 1q(x) = –5(x + 10)2 – 1s(x) = –(x – 1)2 + 0.5g(x) = 2x2 + 10x – 35t(x) = –2x2 – 4x – 3

A
p(x) = 14(x + 7)2 + 1
B
q(x) = –5(x + 10)2 – 1
C
s(x) = –(x – 1)2 + 0.5
D
g(x) = 2x2 + 10x – 35
E
t(x) = –2x2 – 4x – 3
12

When Nick checked his work it did not match the standard form function. Analyze Nick’s work. What was his mistake?

A
In step 1, he did not put the function in standard form correctly.
B
In step 2, he should have also factored –7 from the constant term, 17.
C
In step 3, he did not subtract –7(9) to keep the function equivalent.
D
In step 4, he did not write the perfect square trinomial correctly as a binomial squared.
13

Compare the graphs that Jennifer and Matt drew by completing the statements.

Answers:
Jennifer’s graph is vertically shifted from Matt’s graph.:2 units down
Jennifer’s graph is horizontally shifted from Matt’s graph.:0 units left or right
Jennifer’s graph is Matt’s graph.:the same shape as
Which graph has a vertex that is a maximum?:Neither Jennifer’s nor Matt’s
14

✔ 0 units left or right1 unit left1 unit right

A
✔ 0 units left or right
B
1 unit left
C
1 unit right
15

narrower than wider than ✔ the same shape as

A
narrower than
B
wider than
C
✔ the same shape as
16

Jennifer’sMatt’s✔ Neither Jennifer’s nor Matt’s

A
Jennifer’s
B
Matt’s
C
✔ Neither Jennifer’s nor Matt’s

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