I use the standard orientation of the three coordinate axes.
* - - - - - - y
It is a paraboloid. Consider the following surface: .
What's this surface called?
is the -plane (the "floor" of the graph). What coordinate plane does define?
The -plane is the "left wall" of the graph. What's the trace of this surface in the -plane look like?
Let and we have: .
This is a parabola on the "left wall", vertex at the origin,
. . opening in the positive -direction.
What's the trace of this surface in the planes look like?
Let . .We have: .
These are circles: centered on the -axis with radius