The equation for finding the y-value of the directrix is:

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If you *don't* want to use the formula, there is a simple way to find the "y" value of the directrix.

As stated before, the vertex is halfway between the directrix and the focus.

We've already calculated the "y" values of

the vertex (-5.125) and

the focus (-5)

The difference between these numbers is .125.

In the equation 2x^{2} -3x -4 =0, the "a" value is greater than zero so the directrix is *below* the vertex.

Therefore, the "y" value of the directrix is -5.125 *minus* .125 = -5.25.

(If this equation had a negative value of "a", we would have *added* the .125 value because in that case, the directrix would be *above* the vertex).

As you probably have noticed, once you have calculated the focus or the vertex, just take the "x" value and you have the "x" value of the *axis of symmetry*.