Hey jv,
There is more than one way to approach this, so here is one way. Remember that a parabola is a curve consisting of all points in the coordinate plane that are the same distance from a given point (the
focus) and a given line (the
directrex). The
focal length is the distance from the
vertex to the
focus.
Examples with solutions can be found
here, as well as a number of other places on the net.
$\displaystyle y = 4x^2 + 8x + 5$
First, put the equation in this form: $\displaystyle y=a(x-h)^2+k$
You'll have to know how to complete the square. Do you?
I'll get you started:
$\displaystyle y=4(x^2+2x+ ??)+5-4(??)$
Once you have it in the above form, apply the following information to find what you need:
Vertex $\displaystyle (h, k)$
Focus $\displaystyle \left(h, k+\frac{1}{4a}\right)$
Directrex $\displaystyle y=k-\frac{1}{4a}$