Holiday Bulb (AR Modeling Challenge)
In this GeoGebra Augmented Reality modeling challenge, the goal here is to author 2 surface equations (with domain restrictions) to model the holiday bulb seen in the screencast below.
Modeling Clues:
1) Both surfaces are paraboloids of revolution (where cross sections parallel to the xy-plane are circles).
2) The blue surface has vertex (0,0,5). The pink surface has vertex (0, 0, -3).
3) Both surfaces meet on the xy-plane itself (with no overlap).
4) The point (-1, 1, 3.4) lies on the blue surface.
Additional Challenge:
As you can see from the screencast, these 2 surfaces better model this surface at the upper and lower ends vs. the lower-middle (where it's widest). What other quadric surface model(s) could we use to better model these holiday bulbs?