Algebra: Dilations of Quadratic Functions

Mark ALL that apply!

What transformation has occurred form the quadratic parent function.

f(x) = 2(x - 8)² + 7

• Reflect across the x - axis

• Vertical Stretch

• Right Eight

• Left Eight

• Up Seven

• Reflect across the x - axis

• Vertical Compression

• Right Three

• Up  Three

• Down Three

Which equation will match the following transformations?

- vertical stretch

- up 3

- right 7

• y = -2(x - 7)² + 3

• y = 2(x - 7)² + 3

• y = 2(x - 7)² - 3

• y = 2(x + 7)² + 3

If red represents y = x², which equation represents blue?

• y = 2x²
• y = -2x²
• y = -x²
• y = (x - 1)²

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

• g(x) = x² - 5
• g(x) = x² + 5
• g(x) = (x - 5)²
• g(x) = (x + 5)²

What is the green dashed line called?

• roots or x-intercepts

• parabola

• axis of symmetry

• vertex

• g(x)=2x²
• g(x)=0.5x²
• g(x)=x²+2
• g(x)=(x+2)²

Describe the transformations from the original parent function f(x) = x².

g(x) = 5x² + 2

• Vertical Compression of 5

  Translated Down 2

• Vertical Compression of 5

  Translated Up 2

• Vertical Stretch of 5

  Translated Up 2

• Vertical Shrink of 5

  Translated Down 2

Compare the function y = 5x² to the parent function y = x²

• Wider
• Narrower

• Horizontal compression by 1/2
  Vertical Translation Down 3

• Horizontal compression by 2
  Vertical Translation Up 3

• Horizontal compression by 2
  Vertical Translation Down 3

• Horizontal stretch by 1/2
  Vertical Translation Down 3