Match Quadratic Equation to Graph

Match the description to its equation.
Moves down 1
Moves right 1

• A

• B

• C

• D

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

• a reflection across the line x = -4

• a reflection across the line y = -4

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

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

Pablo throws a ball with a path of
h = -5(t - 2)².
Maria throws a ball with a path of
h = -5(t - 2)² + 10.
Which description is reasonable for the difference in the two equations?

• Maria throws the ball 10 times harder than Pablo does.

• Maria starts her ball at a height 10 feet higher than Pablo does.

• Pablo throws the ball 10 times harder than Maria does.

• Pablo starts his ball at a height 10 feet higher than Maria does.

Match the equation to its description.

• Reflected over x and up 4

• Reflected over x and down 4

• Reflected over x and right 4 

• Reflected over x and left 4

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

• Compress by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• Compress by 5, shifted 2 units left and 2 down

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

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

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

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

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

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

• shifted up 8 units

• shifted down 8 units

• shifted left 8 units

• shifted right 8 units

Match the description to its equation.
- moves down 3

• A

• B

• C

• D

How do the graphs of the functions
f(x) = x² + 9 and
g(x) = x² – 11 relate to each other?

• The graph of f(x) is 2 units above the graph of g(x).

• The graph of f(x) is 20 units above the graph of g(x).

• The graph of f(x) is 2 units to the right the graph of g(x).

• The graph of f(x) is 20 units to the right the graph of g(x).

How is the graph of y = x² different from the graph of
y = 1/3x²?

• The graph of
  y = 1/3x² is shifted up.

• The graph of
  y = 1/3x² is shifted down.

• The graph of
  y = 1/3x² is wider.

• The graph of
  y = 1/3x² is narrower.