Transformations of Quadratic Functions

1.

Multiple Choice

1 min

1 pt

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a translation shifting f(x) 4 units up

a translation shifting f(x) 4 units down

a translation shifting f(x) 4 units to the left

a translation shifting f(x) 4 units to the right

2.

Multiple Choice

1 min

1 pt

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

Wider

Narrower

Vertical translation up by 2 units.

Reflection across the x-axis.

3.

Multiple Choice

1 min

1 pt

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

Translation left 2 units

Narrower

Vertical translation up by 2 units.

Reflection across the x-axis.

4.

Multiple Choice

1 min

1 pt

Which transformation will occur if f(x) = x² is replaced with -f(x)?

Nothing happens, it stays the same.

Narrower

Vertical translation up by 2 units.

Reflection across the x-axis.

5.

Multiple Choice

3 mins

1 pt

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

(-2, 5)

(-6, 5)

(-4, 3)

(-4, 7)

6.

Multiple Choice

1 min

1 pt

If the blue is f(x)=x^2,then the red must be

g(x)=x²-5

g(x)=x²+5

g(x)=(x-5)²

g(x)=(x+5)²

7.

Multiple Choice

3 mins

1 pt

Yes, "+3" on the end of the function moves the function to the right 3 units

No, "+3" on the end of the function moves the function to the left 3 units

No, "+3" on the end of the function moves the function to the down 3 units

No, "+3" on the end of the function moves the function to the up 3 units

8.

Multiple Choice

2 mins

1 pt

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

g(x)=f(x - 3)

g(x)=f(x) - 3

g(x)=f(x) + 3

g(x)=3f(x)

9.

Multiple Choice

2 mins

1 pt

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

g(x)=2f(x)

g(x)=0.5f(x)

g(x)=f(x) + 2

g(x)=f(x + 2)

10.

Multiple Choice

1 min

1 pt

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

g(x)=f(x + 3)

g(x)=f(x - 3)

g(x)=f(x) + 3

g(x)=f(x) - 2

11.

Multiple Choice

2 mins

1 pt

The vertex of the quadratic function f(x) = -2x² + 4x + 3 if (1, 5). If g(x) = f(x - 2), what is the vertex of g(x)

(1, 3)

(1, 7)

(-1, 5)

(3, 5)

12.

Multiple Choice

1 min

1 pt

The vertex of the quadratic function f(x) in the picture (2, -2). If g(x) = f(x) - 4, what is the vertex of g(x)?

(2, -6)

(2, 2)

(-2, -2)

(6, -2)

13.

Multiple Choice

2 mins

1 pt

The vertex of the quadratic function f(x) = -2x² + 4x + 3 is (1, 5). If g(x) = f(x - 2), what is the vertex of g(x)

(1, 3)

(1, 7)

(-1, 5)

(3, 5)

14.

Multiple Choice

2 mins

1 pt

The vertex of the quadratic function f(x) = -x²- 4x + 12 is (-2, 16). If g(x) = f(x) + 3, what is the vertex of g(x)?

(-2, 13)

(-2, 19)

(-5, 16)

(1, 16)

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