(03.09 mc) derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. put the equation in standard form

Check the picture below.

so the focus point is at -2, 4 and the directrix is at y = 6, now, keeping in mind that the vertex is half-way between those two fellows, from 4 to 6, it'd be the y-coordinate of 5, and therefore, the vertex is at -2,5, as you see there in the picture, and the parabola looks like so.  Since the parabola is a vertical one, the squared variable is the "x".

notice the distance "p", is just 1 unit, however, since the parabola is opening downwards, "p" is negative, and thus -1.