Originally Posted by

**galactus** I just showed. It's the same distance as from the vertex to the directrix.

$\displaystyle \frac{1}{4a}=p$. |p| is the distance from the vertex to the focus.

'a' is the coefficient of the x^2. Remember, we had -1/6 on the one I graphed. So, $\displaystyle \frac{1}{4(-1/6)}=|\frac{3}{2}|$

It's 3/2 units from the focus to the vertex or from the vertex to the directrix.

If p<0, then the parabola opens down. If p>0, then it opens up.

Of course, they can be horizontal too. In that case, you have

$\displaystyle x=\frac{1}{4p}y^{2}$ instead of $\displaystyle y=\frac{1}{4p}x^{2}$

If it's a horizontal parabola, then if p>0 it opens to the right and if p<0 it opens left.