y = 4x^2 + 8x + 5
find the focal length, the focus and the directrix.
any help? much appreciated
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.
First, put the equation in this form:
You'll have to know how to complete the square. Do you?
I'll get you started:
Once you have it in the above form, apply the following information to find what you need: