1. The problem asks to determine the coordinates of the vertex of the parabola shown on the graph. 2. The vertex of a parabola given by the equation $y = ax^2 + bx + c$ is found using the formula for the x-coordinate of the vertex: $$x = -\frac{b}{2a}$$. 3. The y-coordinate of the vertex is found by substituting this x-value back into the equation. 4. However, since the graph is given and the vertex is visually identified at approximately $(4, -6)$, we can directly state the vertex coordinates. 5. Therefore, the vertex of the parabola is at the point $$\boxed{(4, -6)}$$. 6. This means the parabola reaches its minimum value at $x=4$ and $y=-6$ because it opens upward.