A parabola is an aesthetically-pleasing graph, perhaps as a result of its symmetry. Nature must think so too (assuming Nature thinks, which It most likely does not), since the parabolic shape occurs naturally in projectile motion and certain orbital paths. Man has found the shape useful as well, using it to create satellite antennas, light reflectors, parabolic cookers, and architectural adornments. Your job is to find some digital images of these natural or man-made parabolas and write a quadratic function for it.

Formally conceived with the use of Geometer's Sketchpad v5 (now defunct), I have adapted this parabolic quest to Geogebra...

Beware of the Catenary

A case of mistaken identity, the catenary is not, in fact, a parabola. It is however hyperbolic. As in hyperbolic cosine. Singingbanana. Duration_4_13