1. 2.1 Transformations of Quadratic Functions

2. Quadratic Functions
A quadratic function is a function that can be written in the form
The U-shaped graph of a quadratic function is called a parabola:

3. Translations and Transformations
reflection in the x-axis and/or a vertical stretch or shrink
horizontal translation
vertical translation

4. Horizontal Translations
Parent function:
Horizontal Translation:
shift left when
shift right when

5. Vertical Translations
Parent function:
Vertical Translation:
shift down when
shift up when

6. Example 1
Describe the transformation of represented by Then graph each function.
5 units down
3 units left

7. Reflections in the x-Axis
Parent function:
Reflection:
Flips over the x-Axis

8. Reflections in the y-Axis
Parent function:
Reflection:
is its own reflection in the y-axis

9. Horizontal Stretches and Shrinks
Parent function:
Horizontal Stretch/Shrink:
horizontal stretch (away from y-axis) when
horizontal shrink (toward y-axis) when

10. Vertical Stretches and Shrinks
Parent function:
Vertical Stretch/Shrink:
vertical stretch (away from x-axis) when
vertical shrink (toward x-axis) when

11. Example 2a
Describe the transformation of represented by . Then graph each function. a.

12. Example 2b
Describe the transformation of represented by . Then graph each function. b.

13. Example 3
Let the graph of be a vertical stretch by a factor of 5 and a reflection in the x-axis, followed by a translation 1 units down of the graph of Write a rule for and identify the vertex.

14. Example 4

15. Example 5

16. Example 5 Continued
+23
+10
+23

17. Example 5 Continued