Question 947097
<br>
The given conditions are those for a parabola with directrix y=4 and focus (0,2).<br>
With directrix at y=4 and focus at (0,2), the parabola opens downward.  The vertex of the parabola is halfway between the focus and directrix, at (0,3).<br>
The vertex form of the equation is<br>
{{{y-k = (1/(4p))(x-h)^2}}}<br>
or<br>
{{{y = (1/(4p))(x-h)^2+k}}}<br>
where (h,k) is the vertex and p is the directed distance (i.e., can be negative) from the directrix to the vertex, or from the vertex to the focus.<br>
The given conditions tell us (h,k) is (0,3) and p is -1.  So the equation is<br>
{{{y = (1/(4(-1)))(x-0)^2+3}}}<br>
or<br>
{{{y = (-1/4)x^2+3}}}<br>