1. Parabolas

2. Unit Vocabulary
Focus- A point that lies on the axis of a parabola, p units from the vertex.
Directrix- line that “underlines” a parabola.
Parabola- Set of all points equidistant from a point called the focus and a line called the directrix.

3. Standard Form: Given on formula sheet:
y – k = (x – h) or x – h = (y – k)2
You are going to change these…..
Multiply both sides by 4p
4p(y – k) = (x – h) and p(x – h) = (y – k)2
YAY!!! NO more fraction!!!

4. VERTICAL vs. HORIZONTAL
Opens
Vertically
Horizontally
Standard Equation
4p(y – k) = (x – h)2
4p(x – h) = (y – k)2
Axis of Symmetery
x = h
y = k
Direction
If p > 0 opens up
If p < 0 opens down
If p > 0 opens right
If p < 0 opens left
Vertex
(h, k)
Focus
(h, k + p)
(h + p, k)
Directrix
y = k - p
x = h - p

5. Find the vertex of the following parabolas and tell which direction they are opening.
1. (x – 3) = (y + 2)2
2. (y + 4) = (x - 9)2
3. (x + 6) = (y + 5)2
4. (y – 7) = (x - 11)2

6. Find the equation of a parabola with the given focus and directrix
focus (-5, 0) and directrix x = 5
focus (12, 0) and directrix x = -12
focus (0, -4) and directrix y = 4
focus (2,2) and directrix y = -2

7. Find the focus and the directrix of the following parabolas.
y – 2 = (x + 7)2
x – 6 = (y - 1)2
x – 7 = (y + 8)2
y + 3 = (x + 1)2

8. Ex. Write the equation of the function in the graph below
9. Directrix y = focus at (-5, -4)

9. Homework
Parabolas
Worksheet