AnswersLUSD-Int Math 2A LT2 Rational and Irrational Numbers A-GCompleting the Square

Completing the Square Answers

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1
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Which statements are true about the graph of the function f(x) = 6x – 4 + x2? Select two options.The vertex form of the function is f(x) = (x – 2)2 + 2.The vertex of the function is (–3, –13).The axis of symmetry for the function is x = 3.The graph increases over the interval (–3, ).The function does not cross the x-axis.

Question illustration
A
The vertex form of the function is f(x) = (x – 2)2 + 2.
B
The vertex of the function is (–3, –13).
C
The axis of symmetry for the function is x = 3.
D
The graph increases over the interval (–3, ).
Option D
E
The function does not cross the x-axis.
2
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Which function in vertex form is equivalent to f(x) = x2 + 6x + 3?

A
f(x) = (x + 3)2 + 3
B
f(x) = (x + 3)2 − 6
C
f(x) = (x + 6)2 + 3
D
f(x) = (x + 6)2 − 6
3

Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Select three options.The function in vertex form is f(x) = (x – 4)2 – 11.The vertex of the function is (–8, 5).The axis of symmetry is x = 5.The y-intercept of the function is (0, 5).The function crosses the x-axis twice.

A
The function in vertex form is f(x) = (x – 4)2 – 11.
B
The vertex of the function is (–8, 5).
C
The axis of symmetry is x = 5.
D
The y-intercept of the function is (0, 5).
E
The function crosses the x-axis twice.
4

What are the coordinates of the vertex of the function f(x)=x2+10x−3?

A
(–5, –28)
B
(–5, 28)
C
(5, –28)
D
(5, 28)
5

An algebra tile configuration. Only the Product spot is shown. 9 tiles are in the Product spot in 5 columns with 5 rows. First row: 1 + x squared, 4 + x. Below the + x squared tile are 4 +x tiles.

Question illustration
A
4
B
8
C
16
D
64
6

An algebra tile configuration. Only the Product spot is shown. 8 tiles are in the Product spot in 4 columns with 4 rows. First row: 1 + x squared, 3 negative x. Second row: 1 negative x, 1 +. Third and fourth rows: 1 negative x.

Question illustration
A
1
B
6
C
8
D
9
7

What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?

A
(6, 31)
B
(−6, 31)
C
(6, −31)
D
(−6, −31)
8

The vertex form of a function is g(x) = (x – 3)2 + 9. How does the graph of g(x) compare to the graph of the function f(x) = x2?

A
g(x) is shifted 3 units left and 9 units up.
B
g(x) is shifted 3 units right and 9 units up.
C
g(x) is shifted 9 units left and 3 units down.
D
g(x) is shifted 9 units right and 3 units down.
9

Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x?

A
f(x) = (x – 8)2 – 56
B
f(x) = (x – 4)2 + 0
C
f(x) = (x + 8)2 – 72
D
f(x) = (x + 4)2 – 32
10

What value for c will make the expression a perfect square trinomial? x2 – 7x + c

A
negative StartFraction 49 Over 4 EndFraction
Option A
B
negative seven-halves
Option B
C
seven-halves
Option C
D
StartFraction 49 Over 4 EndFraction
Option D
11

What are the coordinates of the vertex of the function f(x)=x2+10x−3?

A
(–5, –28)
B
(–5, 28)
C
(5, –28)
D
(5, 28)
12

Which statements are true about the graph of the function f(x) = 6x – 4 + x2? Select two options.

Question illustration
A
The vertex form of the function is f(x) = (x – 2)2 + 2.
B
The vertex of the function is (–3, –13).
C
The axis of symmetry for the function is x = 3.
D
The graph increases over the interval (–3, ).
Option D
E
The function does not cross the x-axis.
13

Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?

A
f(x) = (x – 1)2 + 3
B
f(x) = (x – 1)2 + 5
C
f(x) = (x + 1)2 + 3
D
f(x) = (x + 1)2 + 5
14

The vertex form of a function is g(x) = (x – 3)2 + 9. How does the graph of g(x) compare to the graph of the function f(x) = x2?

A
g(x) is shifted 3 units left and 9 units up.
B
g(x) is shifted 3 units right and 9 units up.
C
g(x) is shifted 9 units left and 3 units down.
D
g(x) is shifted 9 units right and 3 units down.
15

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = –8x + x2 + 7 ?

A
left 4, down 9
B
left 4, up 23
C
right 4, down 9
D
right 4, up 23
16

Which values for h and k are used to write the function in vertex form?

Question illustration
A
h=6, k=36
B
h=−6, k=−36
C
h=6, k=30
D
h=−6, k=−30
17

An algebra tile configuration. Only the Product spot is shown. 9 tiles are in the Product spot in 5 columns with 5 rows. First row: 1 + x squared, 4 + x. Below the + x squared tile are 4 +x tiles.

Question illustration
A
4
B
8
C
16
D
64
18

Charla wants to determine the vertex of the function f(x) = x2 – 18x + 60 by changing the function into vertex form. Which statement about the vertex of the function is true?

A
The x-coordinate of the vertex is greater than the y-coordinate.
B
The x-coordinate of the vertex is negative.
C
The y-coordinate of the vertex is greater than the y-intercept.
D
The y-coordinate of the vertex is positive.
19

An algebra tile configuration. Only the Product spot is shown. 15 tiles are in the Product spot in 6 columns with 6 rows. First row: 1 + x squared, 5 negative x. Below the + x squared tile are 5 negative x tiles. Off to the right are 4 negative tiles in a separate column.

Question illustration
A
4
B
10
C
21
D
25
20

What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?

A
(6, 31)
B
(−6, 31)
C
(6, −31)
D
(−6, −31)

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