1. The vertex of the parabola is at (h, k).

2. Vertex form of a quadratic can be used to determine transformations of the quadratic parent function.
Quadratic parent function: f(x) = x2

3. Horizontal Translations:
If f(x) = (x – 2)2
then for (x – h)2 ,(x – (2))2, h = 2.
The graph moves two units to the right.

4. Horizontal Translations:
If f(x) = (x + 3)2
then for (x – h)2 ,(x – (-3))2 , h = -3
The graph moves three units to the left.

5. Vertical Translations:
If f(x) = (x)2 + 2
then for (x – h)2 + k, (x)2 + 2, k = 2
The graph moves two units up.

6. Vertical Translations:
If f(x) = (x)2 – 1
then for (x – h)2 + k, (x)2 – 1, k = -1
The graph moves one unit down.

7. Horizontal and Vertical Translations:
If f(x) = (x – 3)2 + 1
then for (x – h)2 + k, (x – (3))2 + 1, h = 3 and k = 1
The graph moves three units right and 1 unit up.

8. Horizontal and Vertical Translations:
If f(x) = (x + 1)2 – 2
then for (x – h)2 + k, (x – (-1))2 – 2, h = -1 k = -2
The graph moves one unit left and two units down.

9. Horizontal and Vertical Translations:
The vertex of a parabola after a translation is located at the point (h, k).
If f(x) = (x + 7)2 + 3
then for (x – h)2 + k, (x – (-7))2 + 3, h = -7 k = 3.
The translated vertex is located at the point (-7, 3).

10. Reflection:
If a is positive, the graph opens up.
If a is negative, the graph is reflected over
the x-axis.

11. Vertical Stretch/Compression:
The value of a is not in the parenthesis: a(x)2.
If |a| > 1, the graph stretches vertically away from the x-axis.
If 0 < |a| < 1, the graph compresses vertically toward the x-axis.
f(x) = 2x2 , a = 2, stretch vertically by factor of 2.

15. Horizontal and Vertical Stretch/Compression:
Create a table of values of a horizontal and vertical stretch and compression.

16. Vertical Stretch: f(x) = 2x2 Hor. Compress: f(x) = (2x)21
2(1)2 = 2 2
2(2)2 = 8 3
2(3)2 = 18 x
f(x) 1 2 3
a = 2 x
f(x) 1 2 3
Hor. Compress: f(x) = (2x)2 x
f(x) 1
(2∙1)2 =4 2
(2∙2)2 = 16 3
(2∙3)2 =81

17. HW pg. 320
#’s 23-28, 31, 33-41, 45