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To find the solution set of the quadratic inequality \( f(x) \geq 0 \) from the graph, we need to identify the regions where the function \( f(x) \), represented by the curve, is either zero or positive.

1. **Zeros of the function**: From the graph, we see that \( f(x) = 0 \) at the points \( x = -2 \) and \( x = 2 \), which are the x-intercepts.

2. **Positive values**: The function \( f(x) \) is positive above the x-axis. Looking at the graph, this occurs when \( x \in [-2, 2] \), meaning the graph is at or above the x-axis within this interval.

### Therefore, the solution set for the inequality \( f(x) \geq 0 \) is:

\[
x \in [-2, 2]
\]

Would you like further details or explanations on any specific part of the solution?

Here are 5 related questions you might consider:
1. How would you solve the same inequality if the quadratic function were given as an equation instead of a graph?
2. Can you describe the properties of quadratic functions based on their graph (vertex, direction)?
3. How would you find the vertex of a quadratic function algebraically?
4. What would change in the solution set if the inequality were \( f(x) > 0 \) instead of \( f(x) \geq 0 \)?
5. How do you determine the range of a quadratic function from its graph?

**Tip**: Always check for the intervals where the function crosses the x-axis when solving inequalities involving graphs.

What is the solution set of the quadratic inequality f(x) ≥ 0?

Explore how to find the solution set of the quadratic inequality f(x) ≥ 0 by analyzing the graph. Learn key concepts related to quadratic functions, their x-intercepts, and intervals where the function is positive. Suitable for students in Grades 9-11.

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