1. The problem is to find the coordinates of the vertex of a quadratic function whose graph is a parabola opening downwards with an approximate vertex at (3, 6). 2. The vertex form of a quadratic function is given by $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. 3. Since the parabola opens downwards, the coefficient $a$ is negative. 4. From the graph description, the vertex is at $(3, 6)$, so $h = 3$ and $k = 6$. 5. Therefore, the coordinates of the vertex are exactly $$\boxed{(3, 6)}$$. This is the highest point on the parabola, confirming the vertex coordinates.