Originally Posted by
masters You're probably used to seeing the quadratic written in vertex form like:
$\displaystyle y=a(x-h)^2+k$
$\displaystyle y = x^2 -5x + 4$
Now, just complete the square:
$\displaystyle y=\left(x^2-5x+\frac{25}{4}\right)-\frac{25}{4}+4$
$\displaystyle y=\left(x-\frac{5}{2}\right)^2-\frac{9}{4}$
Vertex $\displaystyle (h, k) = \left(\frac{5}{2}, -\frac{9}{4}\right)$
Directrix:
$\displaystyle y=k-\frac{1}{4a}$
Focus:
$\displaystyle \left(h, k+\frac{1}{4a}\right)$
Roots (zeros):
$\displaystyle x^2-5x+4=0$
Factor and solve for x.