How do I find vertices of a curve and a hyperbola?

Question

This may help:

http://www.mathwords.com/v/vertices_of_a_hyperbola.htm

The vertex is where the tangent to the curve chages direction most rapidly. When the curve is symmetric about vertical or horizontal axis, all you have to do is find where the slope is zero or infinity (respectively), since that will be where the curve changes slope most rapidly. For functions with xy terms in the equations, the axis of symmetry will be tilted and it will be harder to do.