Completing the Square (Continued) Answers

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What is the first step in writing f(x) = 6x2 + 5 – 42x in vertex form?

A
Factor 6 out of each term.
B
Factor 6 out of the first two terms.
C
Write the function in standard form.
D
Write the trinomial as a binomial squared.
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

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
4

Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2?

A
g(x) = –9(x + 1)2 – 7
B
g(x) = 4(x – 3)2 + 1
C
g(x) = –3(x – 4)2 – 6
D
g(x) = 8(x – 3)2 – 5
5

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.
6

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.
7

What is the vertex of g(x) = 8x2 – 64x?

A
(4, –128)
B
(–4, –128)
C
(4, –16)
D
(–4, –16)
8

What is f(x) = 8x2 + 4x written in vertex form?

A
f(x) = 8 –
Option A
B
f(x) = 8 –
Option B
C
f(x) = 8 – 2
Option C
D
f(x) = 8 – 4
Option D
9

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
10

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.

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