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Semicubical parabola
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<iframe 
    src="https://jsxgraph.uni-bayreuth.de/share/iframe/semicubical-parabola" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Semicubical parabola" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    function initboard () {
        var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-1, 2, 3, -2], keepaspectratio: true, axis: true });
        board.suspendUpdate();
        var a = board.create('slider', [[-0.5, 1.8], [1, 1.8], [-5, 0.20, 5]], { name: 'a' });
    
        var p = board.create('curve',
                 [function(t) { return t * t; },
                  function(t) { return a.Value() * t * t * t; },
                  -2, 2
                 ], { strokeWidth: 1, strokeColor: 'black' });
        board.unsuspendUpdate();
    }
    
    initboard();
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

function initboard () {
    var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-1, 2, 3, -2], keepaspectratio: true, axis: true });
    board.suspendUpdate();
    var a = board.create('slider', [[-0.5, 1.8], [1, 1.8], [-5, 0.20, 5]], { name: 'a' });

    var p = board.create('curve',
             [function(t) { return t * t; },
              function(t) { return a.Value() * t * t * t; },
              -2, 2
             ], { strokeWidth: 1, strokeColor: 'black' });
    board.unsuspendUpdate();
}

initboard();
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Semicubical parabola" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   function initboard () {
       var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-1, 2, 3, -2], keepaspectratio: true, axis: true });
       board.suspendUpdate();
       var a = board.create('slider', [[-0.5, 1.8], [1, 1.8], [-5, 0.20, 5]], { name: 'a' });
   
       var p = board.create('curve',
                [function(t) { return t * t; },
                 function(t) { return a.Value() * t * t * t; },
                 -2, 2
                ], { strokeWidth: 1, strokeColor: 'black' });
       board.unsuspendUpdate();
   }
   
   initboard();
</jsxgraph>
A semicubical parabola is a curve defined parametrically as $$x = t^2$$ $$y = at^3$$ **From Wikipedia** The semicubical parabola was discovered in 1657 by William Neile who computed its arc length; it was the first algebraic curve (excluding the line) to be rectified. It is unique in that a particle following its path while being pulled down by gravity travels equal vertical intervals in equal time periods. **From MathDL** 1659: Hendrik van Heuraet sent van Schooten his rectification of the semi-cubical parabola. This was published---his only publication---in the second Latin edition of Descartes' Geometrie. This broke the spell of Aristotle's dictum that curved lines could not in principle be compared with straight lines. 
// Define the id of your board in BOARDID

function initboard () {
    var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-1, 2, 3, -2], keepaspectratio: true, axis: true });
    board.suspendUpdate();
    var a = board.create('slider', [[-0.5, 1.8], [1, 1.8], [-5, 0.20, 5]], { name: 'a' });

    var p = board.create('curve',
             [function(t) { return t * t; },
              function(t) { return a.Value() * t * t * t; },
              -2, 2
             ], { strokeWidth: 1, strokeColor: 'black' });
    board.unsuspendUpdate();
}

initboard();

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.