https://file.aiquickdraw.com/mathbot/file/17262737754330pazhfs9.jpg

Let's analyze the graph and the problem provided:

### Step 1: Identifying \( x \)-intercepts (Solutions to \( f(x) = 0 \))
The \( x \)-intercepts are where the graph of \( f(x) \) crosses the \( x \)-axis, meaning \( f(x) = 0 \) at those points.

From the graph:
- The curve crosses the \( x \)-axis at approximately \( x = 1 \), \( x = 3 \), and \( x = 5 \).

Thus, the solutions to \( f(x) = 0 \) are \( x = 1, 3, 5 \).

### Step 2: Solving \( f(x) \geq 0 \)
We need to find where the graph is on or above the \( x \)-axis (i.e., \( f(x) \geq 0 \)).

Looking at the graph:
- The function is above or on the \( x \)-axis between \( x = 1 \) and \( x = 3 \), and again from \( x = 5 \) onward.

Thus, the solution to \( f(x) \geq 0 \) is:
- \( [1, 3] \cup [5, \infty) \) in interval notation.

### Answers:
- Solutions to \( f(x) = 0 \): \( 1, 3, 5 \)
- Solutions to \( f(x) \geq 0 \) in interval notation: \( [1, 3] \cup [5, \infty) \)

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

Here are 5 related questions to deepen your understanding:
1. How would the solution change if the graph had a negative parabola?
2. What is the significance of the \( x \)-intercepts in solving inequalities like \( f(x) \geq 0 \)?
3. How can you verify the solutions to \( f(x) = 0 \) algebraically if the function is known?
4. What are the different types of solutions for \( f(x) \leq 0 \)?
5. How can you apply this concept to real-world problems involving inequalities?

**Tip:** When solving inequalities graphically, always look for where the function is on or above (or below) the \( x \)-axis depending on the inequality sign.

Refer to the graph of f(x) shown below. The solutions of the equation f(x) = 0 are the x-intercepts of the graph of f. The solution of the inequality f(x) ≥ 0 is the set of x-values at which the graph of f is on or above the x-axis.

Learn how to find x-intercepts and solve inequalities using a graph of the function f(x). This problem helps students understand key concepts in graphing, function analysis, and solving f(x) ≥ 0. Suitable for high school students in Grades 9-12.

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