Conjecture & Proof - the Geometric Parabola.[br][br]Here we generate a quadratic expression from 3 terms of a geometric sequence.[br]Choose the first term and the ratio (multiplier) for the sequence.[br]Construct the quadratic [math]y=ax^2+2bx+c[/math]

Hint[br][br]For the proof of this you might want to try to generalise the geometric terms.[br][br]Using a first term [math]a[/math] and a ratio [math]r[/math]giving three terms [math]a, ar, ar^2[/math][br][br]Now consider the root of the quadratic [math]y=ax^2+2arx+ar^2[/math]