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

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''y = a (x-v_x)^2 + v_y''.
 
''y = a (x-v_x)^2 + v_y''.
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 +
''a'' can be determined by solving
 +
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''p_y = a (p_x-v_x)^2 + v_y'' for ''a''.
  
  

Revision as of 12:31, 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

y = a (x-v_x)^2 + v_y.

a can be determined by solving

p_y = a (p_x-v_x)^2 + v_y for a.


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();
             }]);