Affine normalform of parabola

The underlying JavaScript code

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 16;
JXG.Options.line.strokeWidth = 1;

var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-2, 5, 8, -5], axis: true, showClearTraces: true});

var a = board.create('slider', [[3,4],  [6,4],   [-4, 2, 4]], {name: 'a'});
var b = board.create('slider', [[3,3.5],[6,3.5], [-4, 1, 4]], {name: 'b'});
var c = board.create('slider', [[3,3],  [6,3],   [-4, 1, 4]], {name: 'c'});
var d = board.create('slider', [[3,2.5],[6,2.5], [-4, -1, 4]], {name: 'd'});

var Q3 = board.create('functiongraph', ['x^2']);
var x = board.create('glider', [2, 4, Q3], {name:'x', trace:true});
var t = board.create('point', [1, 0], {name:'t'});
board.create('arrow', [[0,0], t]);

var y = board.create('point', [
            () => a.Value() * x.X() + b.Value() * x.Y() + t.X(),
            () => c.Value() * x.X() + d.Value() * x.Y() + t.Y()
        ], {name: 'y', color:'orange', trace: true});

var txt = board.create('text', [5, -1, () =>
  '$$\\begin{pmatrix}' + a.Value().toFixed(2) + '&' + b.Value().toFixed(2) + '\\\\' +
                         c.Value().toFixed(2) + '&' + d.Value().toFixed(2) + '\\end{pmatrix}$$'], {useMathJax:true});