AnswersAlgebra III AQuadratic Functions: Factored Form

Completing the Square (Continued) Answers

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What is the vertex of g(x) = –3x2 + 18x + 2?

A
(3, –25)
B
(–3, –25)
C
(3, 29)
D
(–3, 29)
2
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What is the vertex of g(x) = 3x2 − 12x + 7?

A
(−6, −5)
B
(−2, −5)
C
(2, −5)
D
(6, −5)
3

Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three options.

A
The graph of f(x) = x2 is shifted down 50 units.
B
The graph of f(x) = x2 is shifted up 50 units.
C
The graph of f(x) = x2 is shifted left 10 units.
D
The graph of f(x) = x2 is shifted right 10 units.
E
The graph of f(x) = x2 is reflected over the x-axis.
4

What is f(x) = 2x2 + 28x – 5 written in vertex form?

A
f(x) = 2(x + 7)2 – 19
B
f(x) = 2(x + 7)2 – 103
C
f(x) = 2(x + 14)2 – 14
D
f(x) = 2(x + 14)2 – 98
5

The function g(x) = 10x2 – 100x + 213 written in vertex form is g(x) = 10(x – 5)2 – 37. Which statements are true about g(x)? Select three options.

A
The axis of symmetry is the line x = –5.
B
The vertex of the graph is (5, –37).
C
The parabola has a minimum.
D
The parabola opens up.
E
The value of a, when the equation is written in vertex form, is negative.
6

What is the vertex of g(x) = 8x2 – 48x + 65?

A
(–3, –7)
B
(3, –7)
C
(24, –7)
D
(–24, –7)
7

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –3x2 – 36x – 60?

A
The graph of f(x) = x2 is made narrower.
B
The graph of f(x) = x2 is shifted right 6 units.
C
The graph of f(x) = x2 is shifted down 48 units.
D
The graph of f(x) = x2 is reflected over the y-axis.
8

Which statement is true concerning the vertex and the axis of symmetry of g(x)=5x2−10x?

A
The function written in vertex form is g(x)=5(x−1)2−5. The vertex is at (1, –5) and the axis of symmetry is x=1.
B
The vertex is at (1, –5) and the axis of symmetry is y = 1.
C
The vertex is at (0, 0) and the axis of symmetry is x = 1.
D
The vertex is at (0, 0) and the axis of symmetry is y = 1.
9

The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.f(x) = 3(x2 – 8x) + 10 = 16

Question illustration
A
f(x) = 3(x + 4)2 – 6
B
f(x) = 3(x + 4)2 – 38
C
f(x) = 3(x – 4)2 – 6
D
f(x) = 3(x – 4)2 – 38
10

Which is one of the transformations applied to the graph of f(x)=x2 to produce the graph of g(x)=2x2−28x+3?

A
shifted up 3 units
B
shifted left 7 units
C
shifted right 7 units
D
shifted down 3 units

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