Name:____________________________________________ Date:___________________ Period:___
Transformation of Quadratic Functions
1. Write the vertex form of a quadratic function.
2. Being specific, name 3 ways that a parabola changes with different types of "a" values.
3. What does changing the "h" variable do to the graph of a quadratic function?
4. What does changing the "k" variable do to the graph of a quadratic function?
5. Using the graph of 𝑓(𝑥) = 𝑥 2 as a guide, describe the transformations, and then graph each function.
a.
b. 𝑦 = 𝑥 2 − 2
𝑦 = 𝑥2 + 2
c.
𝑦 = 2𝑥 2
d.
𝑦=
1 2
𝑥
2
𝑦 = (𝑥 − 2)2
𝑦 = (𝑥 + 2)2
𝑦 = (𝑥 − 1)2 + 1
𝑦 = (𝑥 − 1)2 − 1
𝑦 = 2(𝑥 − 2)2
𝑦 = −2(𝑥 + 1)2 − 1
Write the quadratic function, in vertex form, for each graph.
8.
9.
10.
11.
11.
12.
Graph the quadratic function. Describe the transformation from the parent function𝑦 = 𝑥 2 .
13. 𝑦 = 𝑥 2 − 4
14. 𝑦 = 2𝑥 2 − 2
15. 𝑦 = −𝑥 2 + 2
16. 𝑦 = (𝑥 − 1)2 + 1