Transformation of a Quadratic Function

By the end of this lesson you will be able to:

  • Graph and identify quadratic functions using a vertical shift.
  • Graph and identify quadratic functions using a horizontal shift.
  • Graph and identify quadratic functions using a stretch or shrink.

Parent Function:

Vertical Shift

Horizontal Shift

Student Response #1

In your own words describe the difference between a vertical and horizontal shift on the parent function.

Create a quadratic function with a slider that has a vertical shift between 3 units up and down, and a horizontal shift between 2 units left and right.

Student Construction #1

Vertical Stretch

Student Response #2

The previous slider was an example of a vertical stretch. What would you do to a quadratic function to create a vertical shrink?

Student Construction #2

Construct a slider that would show a vertical stretch between 1/16 and 1/2.
  • Observe the given point.
  • Drag it on the slider and notice the change in the function.
  • Notice the change in point A.

Point A

Where would point A (1, 1) be located on a the given quadratic function:

Write a Quadratic Function

Write a quadratic function after a transformation of 6.5 units up, 7 units left, and vertical stretch of 4.


Now it is your turn to play around with a quadratic funtion. Create your own function:
  • Try to reflect your function over the y-axis
  • Hint: It might be helpful to transform your original function left or right before you try to reflect over the y-axis.