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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.

What is the solution set of the quadratic inequality f(x) ≤ 0 based on the given graph?

Learn how to solve quadratic inequalities using graph interpretation. In this example, we analyze the solution set of f(x) ≤ 0 by identifying the intervals where the graph of the quadratic function is below or on the x-axis.

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