# Transformation of a Quadratic Function

- Author:
- Darby Bjorgan

## 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.

## Playground

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.