A Paraboloid

is a quadric surface that has exactly one axis of symmetry and no center of symmetry.

\(z=\frac{x^2}{a^2} +\frac{y^2}{b^2}\); a and b are constants that dictate the level of curvature in the xz and yz planes respectively.

Any cross section will be a parabola, is a useful shape.

Hyperbolic Paraboloid:

\(z=\frac{y^2}{b^2} -\frac{x^2}{a^2}\);

In this position, the hyperbolic paraboloid opens downward along the x-axis and upward along the y-axis (that is, the parabola in the plane x = 0 opens upward and the parabola in the plane y = 0 opens downward).