Completing the Square Answers

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4

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
5

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
8

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
9

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.
10

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.

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