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1) Using Focus and Directrix**

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Example
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We are given a focus of (.75, -5) and a directrix of Y = -5.25**

What is the Quadratic Equation?

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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.

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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.

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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.