1) Using Focus and Directrix
Example
We are given a focus of (.75, -5) and a directrix of Y = -5.25
What is the Quadratic Equation?
Whenever we are given two of these three:
• focus
• vertex
• directrix
We must use this formula to generate a quadratic equation:

Since we are dealing with upward-pointing or downward-pointing parabolas ("U" shaped or "∩" shaped), the "x" value of the focus will always equal the "x" value of the vertex.
Therefore the "x" value of the vertex (or "h") equals .75.
Next we have to determine the "y" value of the vertex (or "k").
(It is important to state this is NOT the value of 'p'.)
We see that the "y" value for the focus is -5 and for the diectrix it's -5.25. The vertex "y" value always lies exactly between the two and so "k" must equal -5.125.
Finally, we calculate "p" using the equations in diagram 2 and we see the distance is .125.
Now, we can enter all this information into the equation in diagram 2.