Quiz about Quadratic Transformation

Question 1

Match the description to its equation.
- moves up 4

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 2

Match the description to its equation.
- moves down 3

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 3

Match the description to its equation.
-Moves left 2

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 4

Match the description to its equation.
Stretches by a factor of 3

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 5

Match the description to its equation.
Moves up 2
Moves left 4

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 6

Which quadratic function is represented by the graph?

Accepted Answer

y = -2(x + 4)² + 5

Answer

y = 2(x - 4)² + 5

Answer

y = 2(x + 4)² + 5

Answer

y = -2(x - 4)² + 5

Question 7

If the blue graph is
f(x) = x²
then the red must be...

Accepted Answer

g(x) = x²- 5

Answer

g(x) = x²+ 5

Answer

g(x) = (x - 5)²

Answer

g(x) = (x + 5)²

Question 8

What transformations have occurred?

Accepted Answer

Right 2 and up 2

Answer

Left 2 and up 2

Answer

Right 2 and down 2

Answer

Left 2 and down 2

Question 9

How did we transform from f(x) =x²

to

g(x) = -3x²

Accepted Answer

reflection x-axis and stretch

Answer

reflection in x-axis and shift down

Answer

reflection x-axis and compression

Question 10

Match the description to its equation.
Moves right 7

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 11

How did we transform from the parent function?

g(x) = -1/5(x - 1)² + 7

Accepted Answer

reflection, compression, horizontal right, vertical up

Answer

compression, horizontal shift left, vertical shift up

Answer

reflection, horizontal shift right, vertical shift down

Answer

no changes were made to y = x²

Question 12

Match the description to its equation:
moves down 3

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 13

In the equation f(x)=5(x+3)²-10 what does the 5 do?

Accepted Answer

stretch by 5

Answer

compress by 5

Answer

Reflect

Answer

Move up 5

Question 14

What is the vertical shift of this equation?
f(x) = -(x + 3)² - 5

Accepted Answer

down 5

Answer

left 5

Answer

right 5

Answer

up 5

Question 15

Does the graph of this equation widen or narrow from the parent function?
g(x) = 3/4 (x - 5)² + 12

Accepted Answer

widen

Answer

neither

Answer

narrow

Question 16

What is the horizontal shift of this equation?
f(x) = 3/4 (x - 5)² + 12

Accepted Answer

right 5

Answer

up 5

Answer

down 5

Answer

left 5

Question 17

What is the vertical shift of this equation?
g(x) = 3/4 (x - 5)² + 12

Accepted Answer

up 12

Answer

down 12

Answer

left 12

Answer

right 12

Question 18

Does the graph of this equation open up or down?
f(x) = -(x + 3)² - 5

Accepted Answer

down

Answer

up

Question 19

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

Accepted Answer

a horizontal translation 4 units to the left

Answer

a vertical translation 4 units up

Answer

a vertical translation 4 units down

Answer

a horizontal translation 4 units to the right

Question 20

What is the vertex form of a quadratic function?

Accepted Answer

f(x) = a(x-h)² + k

Answer

f(x) = 2a(x-h)² + k

Answer

f(x) = (x+h)² + k

Answer

f(x) = a(x-h) - k

Question 21

What is the axis of symmetry in a function?

Accepted Answer

A vertical line that passes through the vertex and divides the parabola in half

Answer

The transformation of the graph

Answer

The vertex, represented by (h,k)

Answer

y = h

Question 22

What is the axis of symmetry in the function f(x) = (x-1)² +2

Accepted Answer

x = 1

Answer

x = -1

Answer

x = 2

Answer

x = -2

Question 23

Identify the vertex of f(x) = -2(x+1)² + 3

Accepted Answer

(-1,3)

Answer

(h,k)

Answer

(3, 1)

Answer

(-1,-3)

Question 24

Does the function y = (x+2)² have a maximum or minimum?

Accepted Answer

Minimum

Answer

Maximum

Answer

Both

Answer

Neither

Question 25

Does the function y = -1/2(x+1)² have a maximum or minimum?

Accepted Answer

Maximum

Answer

Minimum

Answer

Both

Answer

Neither

Question 26

What does the quadratic function that has a vertex of (3,4) look like?

Accepted Answer

y = a(x-3)² + 4

Answer

y = a(x+3)² + 4

Answer

y = -a(x+3) - 4

Answer

y = a(x-3)² - 4

Question 27

What steps transform the graph y = x² to y = 2(x+2)² - 5?

Accepted Answer

Stretch by 2, shifted 2 units left and 5 down

Answer

Compress by 2, shifted 2 units left and 5 down

Answer

Stretch by 5, shifted 5 units left and 2 down

Answer

Compress by 5, shifted 2 units left and 2 down

Question 28

What steps transform the graph y = x² to y = -1/2(x-4)² + 1?

Accepted Answer

Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

Answer

Compressed by 1/2, shifted 4 units right and 1 unit up

Answer

Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

Answer

Stretched by 1/2, shifted 4 units right and 1 unit down

Question 29

Identify the vertex of f(x) = 5(x+6)² - 7

Accepted Answer

(-6,-7)

Answer

(5,6)

Answer

(0,0)

Answer

(6,-7)

Question 30

What steps transform the graph y = x² to y = x² + 8

Accepted Answer

shifted up 8 units

Answer

shifted down 8 units

Answer

shifted left 8 units

Answer

shifted right 8 units

Question 31

What steps transform the graph y = x² to y = (x-4)²

Accepted Answer

Shifted right 4 units

Answer

Shifted down 4 units

Answer

Shifted left 4 units

Answer

Shifted up 4 units

Question 32

Which function's graph has a vertex (3,5) and contains the point (5,13)?

Accepted Answer

y = 2(x - 3)² + 5

Answer

y = 1/10(x + 3)²- 5

Answer

y = 1/10(x - 3)² - 5

Answer

y = 2(x + 3)² + 5

Question 33

Which of the following shows a compression of the parent function?

Accepted Answer

y = 3/5x2

Answer

y = 2x2

Answer

y = -4x2

Answer

y = -x2

Question 34

Which of the following shows a stretch of the parent function?

Accepted Answer

y = -5x2

Answer

y = -x2

Answer

y = 2/5x2

Answer

y = -3/4x²

Question 35

The graph of m(x) = x² was transformed to create the graph of n(x) = x² + 21. Which of these describes the transformation?

Accepted Answer

A vertical shift up 21 units.

Answer

A vertical shift down 21 units.

Answer

A horizontal shift to the right 21 units.

Answer

A horizontal shift to the left 21 units.

Question 36

The graph of g(x) = x² is transformed to create the graph of g(x) = -g(x). Describe the transformation.

Accepted Answer

Reflection in the x-axis.

Answer

Vertical shift up.

Answer

Horizontal shift to the right.

Answer

Horizontal shift to the left.

Question 37

The graph of g(x) = x² is transformed to create the graph of h(x) = 0.5g(x). Describe the transformation.

Accepted Answer

Vertical shrink/compression by a factor of 0.5

Answer

Vertical stretch by a factor of 0.5.

Answer

Horizontal stretch by a factor of 0.5.

Answer

Horizontal shrink/compression by a factor of 0.5.

Question 38

Match the equation to its description.

Accepted Answer

Stretched by 2 and up 4

Answer

Compressed by 2 and up 4

Answer

Stretched by 2 and left 4

Answer

Compressed by 2 and left 4

Question 39

Match the equation to its description.

Accepted Answer

Stretched by 4 and up 4

Answer

Compressed by 4 and up 4

Answer

Stretched by 4 and left 4

Answer

Compressed by 4 and left 4

Question 40

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

Accepted Answer

Vertical translation up by 2 units.

Answer

Nothing happens, it stays the same.

Answer

Vertical stretch by a factor of 2.

Answer

Reflection across the x-axis.

Question 41

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

Accepted Answer

Reflection across the x-axis.

Answer

Nothing happens, it stays the same.

Answer

Vertical stretch by a factor of 2.

Answer

Vertical translation up by 2 units.

Question 42

How did we transform from f(x) =x²tog(x) = -3x²

Accepted Answer

reflection x-axis and vertical stretch

Answer

reflection in x-axis and vertical shift down

Answer

horizontal stretch

Answer

reflection x-axis and vertical compression

Question 43

The axis of symmetry line passes through which point?

Accepted Answer

vertex

Answer

y-intercept

Answer

any random point

Answer

symmetrical point for the vertex

Question 44

Which is the parent function of a parabola?

Accepted Answer

y = x2

Answer

y = 2x² + 3

Answer

y = -x² -4

Answer

y = -x2

Question 45

Which describes the transformation of the graph of f(x) = x² to the graph of g(x) = -4x²

Accepted Answer

Reflected, narrower

Answer

reflected, wider

Answer

shifted down 4 units

Answer

shifted up 4 units

Question 46

What is the vertex of the quadratic function
f(x) = 4x² + 16x + 7?

Accepted Answer

(-2, -9)

Answer

(-0.5, 0)

Answer

(0, 7)

Answer

(-0.5, -3.5)

Question 47

What are the roots of the function shown?

Accepted Answer

(-3, 0) and (1, 0)

Answer

(0, -3) and (1, -4)

Answer

x = 1

Answer

(2, 5) and (-4, 5)

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