Imaginary Roots of a Quadratic Polynomial

The black curve represents a parabola drawn in the x-y plane. The red curve is its "sister function", a parabola defined in the plane perpendicular to the x-y plane, with matching vertices, opening in opposite directions. Drag your mouse around the graph to see the 3D elements in action. Original idea contributed by: Phil Ramsden in the Wolfram Demonstration Project. Geogebra application written by Miguel Bayona.