ANSWER
[tex]x ^{2} = - 4(y - 1).[/tex]
EXPLANATION
Since the parabola has the (0, 0) and the directrix at y=2.
The equation is of the form
[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]
where (h,k) is the vertex.
The vertex is half way between the directrix and the focus.
The vertex will be at (0,1)
and is the distance from the vertex to the focus which is 1.
[tex]{(x - 0)}^{2} = - 4(1)(y - 1)[/tex]
[tex]x ^{2} = - 4(y - 1)[/tex]
