1. The problem asks for the solution set of the quadratic function $f(x)$ where $f(x) = 0$. 2. The solutions to $f(x) = 0$ are the x-values where the graph intersects the x-axis. 3. From the graph description, the parabola opens upwards and crosses the x-axis at approximately $x = 7.5$ and $x = 17.5$. 4. The vertex at $x = 12.5$ is the minimum point and does not intersect the x-axis there. 5. Therefore, the solution set for $f(x) = 0$ is $\{7.5, 17.5\}$. Final answer: $\boxed{\{7.5, 17.5\}}$