The graph you provided shows a quadratic function $y = f(x)$ that opens upwards, indicating that it is a parabola. The quadratic inequality you are asked to solve is $f(x) \leq 0$, which means you are looking for the values of $x$ where the function is less than or equal to zero.

From the graph:

• The function $f(x)$ equals zero at the $x$-intercepts. These occur at $x = 1$ and $x = 3$.
• The function $f(x)$ is less than zero (i.e., below the $x$-axis) between these two points, for values of $x$ in the interval $(1, 3)$.

Therefore, the solution to the inequality $f(x) \leq 0$ is:

$x \in [1, 3]$

This means that the function is either zero or negative for all $x$ in the closed interval from 1 to 3.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this:

1. How do you solve quadratic inequalities algebraically?
2. What is the general form of a quadratic function?
3. How do you find the vertex of a quadratic function?
4. How can you determine the number of real roots of a quadratic equation?
5. How do transformations affect the graph of a quadratic function?

Tip: When analyzing quadratic inequalities graphically, focus on the regions where the graph crosses or lies below/above the $x$-axis to understand the solution set.