Parabolas for days

Here is an interesting exploration about parabolas. This involves a geometric and analytic dynamic representation of a parabola, including analysis of the directrix, focus, line of reflection, and vertex. Another very interesting piece of this exploration is how the vertex changes as a, b, and c vary from our general equation y = ax^2 + bx + c.

This is a gsp file, so in order to open this you must have Geometer Sketch Pad. Sorry for everyone out there who doesn't.

Here is the file. Have fun exploring!