1. Before: March 19, 2018
For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward or downward.
𝑦 = 𝑥
𝑦 = 2 𝑥 2
𝑦 = −0.5 𝑥 2 − 4

2. DURING: Transforming quadratic functions
Learning Target: I can graph and transform quadratic functions.

3. Transforming Quadratic Functions
The quadratic parent function is 𝑓(𝑥) = 𝑥 2 . The graph of all other quadratic functions are transformations of the graph of 𝑓(𝑥) = 𝑥 2 .
For the parent function
f(x) = 𝑥 2 :
The axis of symmetry is x = 0, or the y-axis.
The vertex is (0, 0)
The function has only one zero, 0.

4. Transforming Quadratic Functions
Previously, we learned when a > 0 (positive), the graph of a quadratic function opens upward.
When a < 0 (negative), the graph of a quadratic function opens downward. This change in direction is a transformation: a reflection over the vertex.

5. Transforming Quadratic Functions
The value of a in a quadratic function determines not only the direction a parabola opens, but also the width of the parabola.

6. Transforming Quadratic Functions
If |a| > 1, the transformation is a vertical stretch
If |a| < 1, the transformation is a vertical compression

7. Transforming Quadratic Functions
I Do:
Are the graphs of the functions narrow (stretched) or wide (compressed)?
𝑦 =3 𝑥 2
𝑦 = 0.5 𝑥 2

8. Transforming Quadratic Functions
We Do:
Order the functions from narrowest graph to widest.
𝑦 = − 𝑥 2
𝑦 = 𝑥 2

9. Transforming Quadratic Functions
You Do:
Order the functions from narrowest graph to widest.
𝑦 = 𝑥 2
𝑦 = −2 𝑥 2

10. Transforming Quadratic Functions
The value of c makes these graphs look different. The value of c in a quadratic function determines not only the value of the y-intercept but also a vertical translation of the graph of 𝑦 = 𝑎𝑥 2 up or down the y-axis.

11. Transforming Quadratic Functions
This can also be notated as 𝑦 = 𝑥 2 + 𝑘.
When comparing graphs, it is helpful to draw them on the same coordinate plane.
Helpful Hint

12. Transforming Quadratic Functions
If c > 0, the graph is translated up
If c < 0, the graph is translated down

13. Transforming Quadratic Functions
I Do:
Compare the graph of the function with the graph of the parent function 𝑦 = 𝑥 2 .
1. 𝑦 = − 1 4 𝑥 2 +3

14. Transforming Quadratic Functions
We Do:
Compare the graph of the function with the graph of the parent function 𝑦 = 𝑥 2 .
1. 𝑦 =3 𝑥 2

15. Transforming Quadratic Functions
You Do:
Compare the graph of the function with the graph of the parent function 𝑦 = 𝑥 2 .
1. 𝑦 = − 𝑥 2 − 4