MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Explain how to obtain the graph of the given quadratic function from the graph of y = x^{2}.

1) f(x) = x^{2} – 4

A) Take the graph of y = x^{2} and shift it 4 units to the left.

B) Take the graph of y = x^{2} and shift it 4 units up.

C) Take the graph of y = x^{2} and shift it 4 units down.

D) Take the graph of y = x^{2} and shift it 4 units to the right.

Sketch the graph of the quadratic function.

2) f(x) = x^{2} – 3

A)

B)

C)

D)

Sketch the graph of the quadratic function. Identify the vertex and axis of symmetry.

3) f(x) = x^{2} + 3

A) vertex (-3, 0)

axis of symmetry: x = -3

B) vertex (0, -3)

axis of symmetry: x = 0

C) vertex (0, 3)

axis of symmetry: x = 0

D) vertex (3, 0)

axis of symmetry: x = 3

Explain how to obtain the graph of the given quadratic function from the graph of y = x^{2}.

4) f(x) = (x + 5)^{2}

A) Take the graph of y = x^{2} and shift it 5 units to the left.

B) Take the graph of y = x^{2} and shift it 5 units to the right.

C) Take the graph of y = x^{2} and shift it 5 units down.

D) Take the graph of y = x^{2} and shift it 5 units up.

5) f(x) = (x – 9)^{2} – 3

A) Take the graph of y = x^{2} and shift it 9 units to the right and 3 units up.

B) Take the graph of y = x^{2} and shift it 9 units to the right and 3 units down.

C) Take the graph of y = x^{2} and shift it 9 units to the left and 3 units down.

D) Take the graph of y = x^{2} and shift it 9 units to the left and 3 units up.

Sketch the graph of the quadratic function. Identify the vertex and axis of symmetry.

6) f(x) = (x + 2)^{2}

A) vertex (-2, 0)

axis of symmetry: x = -2

B) vertex (0, -2)

axis of symmetry: x = 0

C) vertex (0, 2)

axis of symmetry: x = 0

D) vertex (2, 0)

axis of symmetry: x = 2

7) f(x) = (x – 7)^{2}

A) vertex: (0, 0)

axis of symmetry: x = 0

B) vertex: (-7, 0)

axis of symmetry: x = -7

C) vertex: (7, 0)

axis of symmetry: x = 7

D) vertex: (0, -7)

axis of symmetry: x = 0

8) f(x) = (x – 11)^{2}

A) vertex: (0, 0)

axis of symmetry: x = 0

B) vertex: (11, 0)

axis of symmetry: x = 11

C) vertex: (0, -11)

axis of symmetry: x = 0

D) vertex: (-11, 0)

axis of symmetry: x = -11

9) f(x) = (x + 6)^{2}

A) vertex: (0, 6)

axis of symmetry: x = 0

B) vertex: (6, 0)

axis of symmetry: x = 6

C) vertex: (0, 0)

axis of symmetry: x = 0

D) vertex: (-6, 0)

axis of symmetry: x = -6

10) f(x) = (x – 6)^{2} + 1

A) vertex (1, 6)

axis of symmetry: x = 1

B) vertex (-6, 1)

axis of symmetry: x = -6

C) vertex (-1, -6 )

axis of symmetry: x = -1

D) vertex (6, 1)

axis of symmetry: x = 6

11) f(x) = (x – 2)^{2} – 4

A) vertex: (- 2, – 4)

axis of symmetry: x = – 2

B) vertex: (2, – 4)

axis of symmetry: x = 2

C) vertex: (- 2, – 4)

axis of symmetry: x = – 2

D) vertex: (2, – 4)

axis of symmetry: x = 2

12) f(x) = (x + 1)^{2} – 9

A) vertex: (- 1, – 9)

axis of symmetry: x = – 1

B) vertex: (1, – 9)

axis of symmetry: x = 1

C) vertex: (1, – 9)

axis of symmetry: x = 1

D) vertex: (- 1, – 9)

axis of symmetry: x = – 1

13) f(x) = (x – 1)^{2} – 1

A) vertex: (- 1, – 1)

axis of symmetry: x = – 1

B) vertex: (1, – 1)

axis of symmetry: x = 1

C) vertex: (- 1, – 1)

axis of symmetry: x = – 1

D) vertex: (1, – 1)

axis of symmetry: x = 1

Explain how to obtain the graph of the given quadratic function from the graph of y = x^{2}.

14) f(x) = 5(x – 3)^{2}

A) Take the graph of y = x^{2} and shift it 3 units to the left and vertically stretch it by a factor of 5

B) Take the graph of y = x^{2} and shift it 3 units to the left and vertically compress it by a factor of 5

C) Take the graph of y = x^{2} and shift it 3 units to the right and vertically compress it by a factor of 5

D) Take the graph of y = x^{2} and shift it 3 units to the right and vertically stretch it by a factor of 5

15) f(x) = -2(x + 9)^{2} + 6

A) Take the graph of y = x^{2} and shift it 9 units to the right, shift it 6 units up, vertically stretch it by a factor of +2, and the graph will open downward.

B) Take the graph of y = x^{2} and shift it 9 units to the left, shift it 6 units up, vertically compress it by a factor of +2, and the graph will open downward.

C) Take the graph of y = x^{2} and shift it 9 units to the left, shift it 6 units up, vertically stretch it by a factor of +2, and the graph will open downward.

D) Take the graph of y = x^{2} and shift it 9 units to the right, shift it 5 units down, vertically stretch it by a factor of +2, and the graph will open upward.

16) f(x) = – (1/2)(x + 8)^{2} + 6

A) Take the graph of y = x^{2} and shift it 8 units to the left, shift it 6 units up, vertically stretch it by a factor of + (1/2), and the graph will open downward.

B) Take the graph of y = x^{2} and shift it 8 units to the left, shift it 6 units up, vertically compress it by a factor of +2, and the graph will open upward.

C) Take the graph of y = x^{2} and shift it 8 units to the left, shift it 6 units up, vertically compress it by a factor of + (1/2), and the graph will open downward.

D) Take the graph of y = x^{2} and shift it 8 units to the right, shift it 6 units down, vertically stretch it by a factor of + (1/2), and the graph will open upward.

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