1. 9.2 Parabolas
Emerald Seing

2. A parabola is defined in terms of a fixed point, the focus, and a fixed line, the directrix. PF=PD meaning that any point on the parabola to the focus is equal to the shortest distance from that point to the directrix.

3. Finding The Equation

4. This is only true for equations with the center at (0,0).

5. Horizontal Directrix Vertical Directrix
The parabola will open either up or down
The equation will have Y by itself on one side
The line of the directrix will cross the Y-axis
The axis of symmetry will be on the Y-axis
Y=…
Vertical Directrix
The parabola will open either right or left
The equation will have X by itself on one side
The line of the directrix will cross the X-axis
The line of symmertry will be on the X-axis
X=…

6. Example One

7. Example Two

8. These equations apply to all parabolas who’s centers are not located at (0,0).

9. Example One

10. Example
Two