A paraboloid is a three-dimensional shape that has two terms of x, y, or z that are squared and one term of x, y, or z that is not. Examples of equations that describe paraboloids are:
ax2 + by2 = z
or az2 - by2 = x
When both squared terms are positive, like in the first equation, the paraboloid is an elliptical paraboloid (shaped like a roundish, eggish blob).
When one squared term is negative and one is positive, like in the second equation, the paraboloid is a hyperbolic paraboloid (shaped like a saddle).