1. **State the problem:** We need to determine the domain on which the given quadratic function is decreasing. 2. **Identify the function type:** The graph is a downward-opening parabola with vertex at approximately $(4, 75)$ and endpoints at $(0, 27)$ and $(9, 0)$. 3. **Recall the properties of a parabola:** For a quadratic function $f(x) = ax^2 + bx + c$ with $a < 0$, the parabola opens downward. - The vertex represents the maximum point. - The function is increasing on the interval to the left of the vertex. - The function is decreasing on the interval to the right of the vertex. 4. **Determine the decreasing interval:** Since the vertex is at $x = 4$, the function decreases for $x > 4$. 5. **Check the domain of the function:** The graph has solid endpoints at $x=0$ and $x=9$, so the domain is $[0,9]$. 6. **Conclusion:** The function is decreasing on the interval $$\boxed{(4, 9)}$$ which matches the given graph information.