Second degree polynomials are also known as quadratic polynomials. Their shape is known as a parabola. Long before the language of algebra was developed the ancient Greeks recognized the parabola as a conic section, and were also able to define it as the collection of all points equidistant from a point (focus) and a line (directrix).
The object formed when a parabola is rotated about its axis of symmetry is known as a paraboloid, or parabolic reflector. Satellite dish antennas typically have this shape. All incoming energy reflects off the dish into the paraboloid's focal point where the signal collection hardware is placed.
Quadratics have these characteristics:
The example shown below is: