Answers26MATH_Recovery_Alg1B22Completing the Square (Continued)

Completing the Square (Continued) — Unit test Answers

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What is the axis of symmetry of h(x) = 6x2 − 60x + 147?

A
x = −5
B
x = −3
C
x = 3
D
x = 5
2
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What is the range of the function f(x) = −(x + 3)2 + 7?

A
all real numbers less than or equal to 7
B
all real numbers greater than or equal to 7
C
all real numbers less than or equal to −3
D
all real numbers greater than or equal to −3
3

Which function has a vertex on the y-axis?

A
f(x) = (x – 2)2
B
f(x) = x(x + 2)
C
f(x) = (x – 2)(x + 2)
D
f(x) = (x + 1)(x – 2)
4

Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Select three options.

A
The domain is {x| x ≥ 3}.
B
The range is {y| y ≥ –1}.
C
The function decreases over the interval (–∞, 3).
D
The axis of symmetry is x = –1.
E
The vertex is (3, –1).
5

Which statements are true about the graph of the function h(x) = –5x2 + 60x – 200? Select three options.

A
The axis of symmetry is the line x = –6.
B
The graph of h(x) will not intersect the graph of the parent function, f(x) = x2.
C
The vertex of the graph is at (6, –20).
D
The parabola has a maximum.
E
The value of k, when the equation is written in vertex form, is –200.
6

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6?

A
left 3 units, down 3 units
B
right 3 units, down 3 units
C
left 6 units, down 1 unit
D
right 6 units, down 1 unit
7

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

A
right 5, down 23
B
left 5, down 23
C
right 5, up 27
D
left 5, up 27
8

The steps in writing f(x)=18x+3x2 in vertex form are shown, but a value is missing in the last step.Write the function in standard form. Factor a out of the first two terms. f(x)=3(x2+6x)Form a perfect square trinomial. f(x)=3(x2+6x+9)−3(9) Write the trinomial as a binomial squared. f(x)=3(x+___)2−27

Question illustration
A
3
B
6
C
9
D
18
9

The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)?

A
g(x) = (x – 2)2 + k
B
g(x) = (x + 8)2 + k
C
g(x) = (x – h)2 – 5
D
g(x) = (x – h)2 – 15
10

Which statements about the function are true? Select three options.

A
The vertex of the function is at (–4,–15).
B
The vertex of the function is at (–3,–16).
C
The graph is increasing on the interval x > –3.
D
The graph is positive only on the intervals where x 1.
E
The graph is negative on the interval x < –4.
11

The graph of the function f(x) = (x + 2)(x − 4) is shown.

Question illustration
A
all real values of x where x < −2
B
all real values of x where −2 < x < 4
C
all real values of x where 1 < x < 4
D
all real values of x where x < 0
12

What is the y-value of the vertex of the function f(x)=−(x−3)(x+11)?

A
−8
B
−4
C
33
D
49
13

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 9x2 – 36x?

A
The graph of f(x) = x2 is widened.
B
The graph of f(x) = x2 is shifted right 4 units.
C
The graph of f(x) = x2 is shifted down 36 units.
D
The graph of f(x) = x2 is reflected over the x-axis.
14

What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)?

A
3
B
6
C
112
D
121
15

Giselle graphs the function f(x) = x2. Robin graphs the function g(x) = –x2. How does Robin’s graph relate to Giselle’s?

A
Robin’s graph is a reflection of Giselle’s graph over the x-axis.
B
Robin’s graph is a reflection of Giselle’s graph over the y-axis.
C
Robin’s graph is a translation of Giselle’s graph 1 unit down.
D
Robin’s graph is a translation of Giselle’s graph 1 unit left.

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