Assume quadratic has the form y=a(x+3)(x-5) where a is a constant.
So y=a(x²-2x-15). Plug in (3,6):
6=a(9-6-15)=-12a, so a=-6/12=-1/2.
So we have y=-(1/2)(x²-2x-15). We need to get this into vertex form so we have to complete the square:
Therefore y=-(x-1)²/2+8, in vertex form: y-8=-(x-1)²/2, where the vertex is (1,8).