1. y = x2 Translations and Transformations Summary
The following summarizes what affect certain changes to the equation y = x2 have on the graphs.
1. y = x2 → - y = x2
reflection in the x axis
y = x y = x2

2. y = x2 Translations and Transformations Summary
2. y = x2 → ? y = x2
vertical stretch = to the reciprocal of the # in front of y
ex. 2 y = x2
v.s. = ½
1/4 y = x2
v.s. = 4
y = x /4 y = x y = x2

3. y = x2 Translations and Transformations Summary
3. y = x2 → y + ? = x2
vertical translation opposite the # added to y
ex. y + 3 = x2
v.t. 3 down
y - 4 = x2
v.t. 4 up
y = x2
y + 3 = x2

4. y = x2 Translations and Transformations Summary
4. y = x2 → y = (x + ?)2
horizontal translation opposite the # added to x
ex. y = (x – 6)2
h.t. 6 right
y = (x + 8)2
h.t. 8 left
y = (x + 8) y = x y = (x – 6)2

5. y = x2 Translations and Transformations Summary
Transformational form of a Quadratic Equation
- a (y + k)= (x + h)2
reflection
v.s. equal to the reciprocal of a
v.t. opposite the # added to y
h.t opposite the # added to x

6. y = x2 Translations and Transformations Summary
Standard form of a Quadratic Equation
y=- a (x + h)2 + k
reflection
v.s. equal to a
h.t. opposite h
v.t equal to k