write a quadratic equation for which the graphs of the equation opens downward, the vertex is (0,3). the domain includes all real numbers, and the range is y<-3.

the vertex is (0,3) so the equation is

y = ax^2 + 3
since it opens downward,any negative value for a will work.
Unfortunately, this has a range of y ≤ 3, not y < -3.
If the vertex is at (0,3), clearly the range includes 3.