Difference between revisions of "Vertex equations of a quadratic function and it's inverse"

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A parabola can be uniquely defined by its vertex ''V'' and one more point ''P''.
 
A parabola can be uniquely defined by its vertex ''V'' and one more point ''P''.
 
The function term of the parabola then has the form
 
The function term of the parabola then has the form
<math>y</math>
+
<math>y=a</math>
  
  

Revision as of 12:28, 16 December 2014

A parabola can be uniquely defined by its vertex V and one more point P. The function term of the parabola then has the form [math]y=a[/math]


JavaScript code

var b = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 5, 5, -5], grid:true});
var v = b.create('point', [0,0], {name:'V'}),
    p = b.create('point', [3,3], {name:'P'}),
    f = b.create('functiongraph', [
             function(x) {
                 var den = p.X()- v.X(),
                     a = (p.Y() - v.Y()) / (den * den);
                 return a * (x - v.X()) * (x - v.X()) + v.Y();
             }]);

})();

JavaScript code

var b = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 5, 5, -5], grid:true});
var v = b.create('point', [0,0], {name:'V'}),
    p = b.create('point', [3,3], {name:'P'}),
    f = b.create('functiongraph', [
             function(x) {
                 var den = p.Y()- v.Y(),
                     a = (p.X() - v.X()) / (den * den);
                 return Math.sqrt((x - v.X()) / a) + v.Y();
             }]);