Graph Quadratic Equations and Transformations

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 description to its equation.
Reflected over the x-axis 
Stretched by a factor of 2

• A

• B

• C

• D

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

• A

• B

• C

• D

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x)=3x²

• g(x)=1/3x²

• g(x) = x² - 3

• g(x) = (x-3)²

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x) = 2x²

• g(x) = 1/2x²

• g(x) = x² + 2

• g(x) = (x + 2)²

• Maximum

• Left 5

• Down 8

• vertical shrink

• Minimum

• Right 5

• Up 8

• Vertical Stretch

• No Vertical Shift

• Maximum

• Left 5

• Down 8

• vertical shrink

• Minimum

• Right 5

• Up 8

• Vertical Stretch

• No Vertical Shift

• Maximum

• Left 5

• Down 8

• vertical shrink

• Minimum

• Right 5

• Up 8

• Vertical Stretch

• No Vertical Shift

• It is reflected across the x-axis.

• It is reflected across the y-axis.

• It is shifted upwards.

• It is shifted downwards.