AnswersAlgebra III ACompleting the Square

Completing the Square Answers

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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)
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

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
4

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.
5

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
6

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

A
right 1 unit
B
left 1 unit
C
right 2 units
D
left 2 units
7

Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Select three options.

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.
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

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)
10

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

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