1. Quadratic Functions, Translation and Reflection
Lesson 2.2

2. Quadratic Function Standard form Vertex form a, b, and c are constants
a ≠ 0 (why?)
Vertex form
(h, k) is the vertex of the parabola
value for a is the same in both forms

3. Vertex of Parabola
X-value of vertex at
Y-value of vertex at
For

4. Translations In the Y= screen, enter the function
Now enter the variations as shown
Predict the results of the variations
Set style:
dotted
thick

5. Horizontal Translations
Shift to the right f(x – a)
Shift to the left f(x + a)

6. Translations Now try … make predictions
These changes created vertical translations
f(x) + a shift up
f(x) – a shift down

7. Translations What about? Predictions?
When a > 1 gives vertical stretch
When 0 < a < 1 gives vertical compression

8. Reflections Make your predictions again for these variations
-f(x) gives reflection in the x-axis
f(-x) gives reflection in y-axis

9. Combinations
Given
What happens when we have these variations?

10. Assignment
Lesson 2.2
Page 79
Exercises 1 – 61 EOO