The general equation is y-k=a(x-h)² where (h,k) is the vertex, so y-6=a(x+7)².
Plug in (3,-5): -11=a(10)² and a=-11/100 so y=-11/100(x+7)²+6=-11/100(x²+14x+49)+6=-11x²/100-77x/50-539/100+6.
So y=-11x²/100-77x/50+61/100. Also written: y=-0.11x²-1.54x+0.61.