1. Do Now:
Think about what you learned from Chapter 1. How do you think the constants a, h, and k affect the graph of the quadratic function y = a(x − h)2 + k?

2. 2.1: Transformationof Quadratic Functions

3. Quadratic Function: y = a(x - h)2 + k Vertex: (h, k)
Parabolic shape (u-shaped)
If a is positive, the parabola will open up, if a is negative it will open down.
Vertical line of symmetry: x = h

4. Transformations of Quadratic Functions
Vertex: (h, k)
Tells if graph
opens up (+)
down (-)
Reflection
Stretch or shrink
Take opposite value
Moves left (+)
Moves right (-)
Tells movement
Up (+)
Down (-)

5. Different Stretches and Shrinks

6. Example: x y Opening: up or down? Left/right transformation:
Stretch/Shrink:
Up/down transformation:

7. Example: g(x) = 2(x)2 + 1 x y Opening: up or down?
Left/right transformation:
Stretch/Shrink:
Up/down transformation:

8. Example: x y Opening: up or down? Left/right transformation:
Stretch/Shrink:
Up/down transformation:

9. Practice x y Opening: up or down? Left/right transformation:
1. Describe the transformation of f (x) = x2 represented by g. Then graph the function.
g(x) = (x + 4) 2 − 1. x y
Opening: up or down?
Left/right transformation:
Stretch/Shrink:
Up/down transformation:

10. Practice g(x) = (x − 3) 2 x y Opening: up or down?
2. Describe the transformation of f (x) = x2 represented by g. Then graph the function.
g(x) = (x − 3) 2 x y
Opening: up or down?
Left/right transformation:
Stretch/Shrink:
Up/down transformation:

11. Practice g(x) = (x − 2) 2 − 2 x y Opening: up or down?
3. Describe the transformation of f (x) = x2 represented by g. Then graph the function.
g(x) = (x − 2) 2 − 2 x y
Opening: up or down?
Left/right transformation:
Stretch/Shrink:
Up/down transformation:

12. Practice g(x) = (x + 5) 2 + 1 x y Opening: up or down?
4. Describe the transformation of f (x) = x2 represented by g. Then graph the function.
g(x) = (x + 5) 2 + 1 x y
Opening: up or down?
Left/right transformation:
Stretch/Shrink:
Up/down transformation:

13. Practice
5. Describe the transformation of f (x) = x2 represented by g. Then graph the function. x y
Opening: up or down?
Left/right transformation:
Stretch/Shrink:
Up/down transformation:

14. Match each quadratic function with its graph. Explain your reasoning
Match each quadratic function with its graph. Explain your reasoning. Then use a graphing calculator to verify that your answer is correct.
1. y = −(x − 2) y = (x − 2) y = −(x + 2)2 − 2
4. y = 0.5(x − 2)2 − y = 2(x − 2) y = −(x + 2)2 + 2

15. Homework
p52, #8, 10, 20, 22, 24
* You will need graph paper

16. Do Now
Describe the transformation of f (x) = x2 represented by g. Then graph each function.
g(x) = −(x + 3)2 + 2 x y

17. Identifying Transformations

18. Practice: Match each function with its graph.

19. CW/HW Classwork Practice B Worksheet
Homework: 2.1 Practice A Worksheet #1, 3, 6, 7, 8