Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1?

So hmm notice the picture below

keep in mind that, the vertex is half-way between the focus point, and the directrix

so.. since the focus is up, and the directrix, down below, that means, the parabola is vertical and opening upwards, thus the squared variable is the "x"

thus 

so.. from half-way of the focus and directrix, you can see what h,k coordinates are for the vertex, and you can also see the "p" distance from the vertex to either, the focus or directrix

so... just plug in those values

The surface area would be 576 because you multiply all the numbers then multiply that number by 6