Question

The graph of a quadratic function is parabola that opens down and has a vertex of (4,3) what is a function of this graph?

Answer 1

y = a(x-h)^2 + k is the general equation of a parabola in the vertex form where (h,k) is the vertex.
If a is positive the parabola opens upward.
If a is negative the parabola opens downward.

You are given the vertex as (4,3). So you know h and k. Choose a = -1 so the parabola opens downward.