1. This isn't really a specific question, but in general, what would be ways to find the vertex of a parabola? (Assuming you know all the necessary information and whatnot)
2. How do you find the directrix of a parabola, and what would be its use?
It depends what form your equation is in.
If it is of the form
Then the vertex is (h,k)
the focal length is |a|
If a is positive then it is concave up, if a is negative then it is concave down.
The focus is (h,k+a) the axis of symmetry is x=h and the directrix is y=k-a
The definition of a parabola is the locus of all points equidistant from a line called the directrix and a point called the focus.
Give the directrix and the focus you can determine the equation of the parabola using locus (which is a fun things to do when you get used to the method)
What would you use the directrix for ? ... not sure what this question is after but if you google it the answer may become clear :/