Custom Made Solid of Revolution

In the applet below, you'll see an image of a vase. [br][br]14 points are plotted along the surface of this vase. [br]You can move these points anywhere you'd like at any time! [br][br]The function drawn below is the function-of-best-fit. [br]You can adjust the degree of this polynomial function by using the [b]degree slider[/b]. [br][br]Can you position the white points and find the best degree of the polynomial of best fit so that the [b][color=#ff00ff]surface of revolution[/color][/b] GeoGebra creates looks most like the vase seen to the left?
Quick (Silent) Demo

Information: Custom Made Solid of Revolution