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.
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.