Identifying quadric surfaces

magic88

Hi there,

I am learning about quadric surfaces in my second year multivariable calculus course.

I would like to know how most people would identify (find the name of) a quadric surface if they had the equation. We only need to know 6 different quadric surfaces, so should I ...

(a) memorize the equations to identify the surface, or
(b) sketch out what the xy-, xz-, and yz-planes look like, sketch out the surface to see what it looks like, then identify it?

What do you do?

Thanks in advance.