To figure out the equation of a parabola we must first understand what is a parabola?
The equation of a parabola has to have the following.
1. Vertex at
2. Focus at
a > 0
x = -a
x > 0
Now let's can derive the following statement
Below is an example of all the parts of teh parabola, from what you can see all the points of the parabola are derived from the focus and the directrix.