Quadratic Function Translations and Dilations

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

Check ALL that apply: What transformations have occured to the function?

• Translation up 2

• Translation right 3

• Horizontally Compressed by 1/3

• Horizontally stretched by 3

• Translated right 9

What is the vertex form of a quadratic function?

• f(x) = ax² + bx + c

• f(x) = a(x-h)² + k

• f(x) = a(x-p)(x-q)

• f(x) = ax + b

What determines the direction of a parabola's opening?

• The value of b

• The value of c

• The sign of the coefficient a

• The value of the vertex

Which transformation involves stretching or compressing the graph?

• Dilation

• Translation

• Reflection

• Rotation

Which transformation involves shifting the graph horizontally or vertically?

• Translation

• Reflection

• Dilation

• Rotation

The point (8, 12) was dilated to become point (2, 3). What was the scale factor?

• ½

• ¼

• 4

• 2

A dilation is which of the following: 

• An enlargement

• A reduction

• Either an enlargement or a reduction

• Neither an enlargement or a reduction

Does the image show a Dilation?

• Yes

• No