Hyperbolic Paraboloid

Equation:   

This is probably the hardest quadric surface to visualize.  The x-axis in the picture ranges from -10 to 10, the y-axis ranges from -20 to 20, and the z-axis ranges from -30 to 30.  Perhaps the easiest way to visualize this is to think of the shape of a saddle.  In the xz-plane, we have a parabola.  In the yz-plane, we have a parabola opening in the opposite direction.  In planes parallel to the xy-plane, we see hyperbolas.