https://file.aiquickdraw.com/mathbot/file/17249426364554ezf0riu.jpg

Select all that apply:

x=1

x=0

x=−6

x=−2

x=4

x=2

To solve the problem, we need to find the values of \(x\) for which \(f(x) = -3\), given the graph of \(y = f(x)\).

### Steps:
1. **Identify the value on the y-axis:** Locate where \(y = -3\) on the graph. This is the horizontal line that crosses the y-axis at \(-3\).

2. **Determine where the graph intersects this line:** Look at the points on the graph where it crosses this line \(y = -3\).

3. **Find the corresponding x-values:** These x-values are the solutions where \(f(x) = -3\).

### Analysis:
- The graph of \(y = f(x)\) appears to intersect the line \(y = -3\) at two points.
- From the graph, the x-values at which \(f(x) = -3\) seem to be \(x = -2\) and \(x = 2\).

### Answer:
The correct answers are:
- \(x = -2\)
- \(x = 2\)

Would you like further details or have any other questions?

Here are 5 related questions to explore further:
1. What are the x-values where \(f(x) = 0\) based on the graph?
2. How can you determine the vertex of the parabola from the graph?
3. What is the equation of the parabola if the vertex is at \((0, -4)\)?
4. How does shifting the graph vertically affect the points where \(f(x) = -3\)?
5. What are the implications of the parabola's symmetry in identifying solutions for \(f(x) = k\)?

**Tip:** When analyzing a parabola, remember that it is symmetric about its vertex, which can help identify solutions quickly.

Discover how to find x-values where f(x) = -3 on a graph with a step-by-step explanation. This problem involves analyzing functions and graph intersections, suitable for high school students.

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