Answer
$(x-800)^2=-200(y-3200)$
Work Step by Step
Step 1. Use the figure given in the Exercise, assume the general equation of the parabola is $(x-h)^2=-4p(y-k)$
Step 2. The vertex $(h,k)$ can be found from the figure as $(800, 3200)$, thus $h=800, k=3200$
Step 3. As the origin is on the parabola, we have $800^2=4p\times3200$ which gives $p=50$
Step 4. Conclusion: the equation of the parabola is $(x-800)^2=-200(y-3200)$
