Semicubical parabola

A semicubical parabola is a curve defined parametrically as

[math]\displaystyle{ x = t^2 }[/math]

[math]\displaystyle{ y = at^3 }[/math]

References

• Wikipedia on semicubical parabola
• MathDL, the MAA Mathematical Sciences Digital Library

The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true, axis:true});
brd.suspendUpdate();
var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});

var p = brd.create('curve',
             [function(t){ return t*t;},
              function(t){ return a.Value()*t*t*t;}
             ],
             {strokeWidth:2, strokeColor:'black'});
brd.unsuspendUpdate();