https://file.aiquickdraw.com/mathbot/file/1727061900979jbs00qyi.jpg

To solve \( f(x) = -2 \) for the graph you uploaded, we need to identify where the curve intersects the line \( y = -2 \). The graph shown is of a parabola, and we need to find the \( x \)-coordinates where the curve touches the line at \( y = -2 \).

### Steps:
1. **Visual Identification**: The graph shows that the parabola is symmetric and opens upward. You can visually observe that the parabola crosses \( y = -2 \) at two points.
2. **Approximation**: The points where the parabola intersects \( y = -2 \) appear to be around \( x = -3 \) and \( x = 1 \).
3. **Exact Solution**: If we had the equation of the parabola, we could solve it algebraically. However, based on the graph, we approximate the solutions as \( x \approx -3 \) and \( x \approx 1 \).

Would you like to confirm or refine these values algebraically or have any more specific questions?

### Related Questions:
1. What is the equation of the parabola shown in the graph?
2. How can we derive the vertex of the parabola from the graph?
3. How do we solve a quadratic equation algebraically to find the points where \( f(x) = -2 \)?
4. Can you explain how to determine the axis of symmetry from a parabola's graph?
5. How can transformations affect the shape and position of a parabola?

**Tip**: To find the exact intersection points of a parabola and a horizontal line, it's helpful to solve the quadratic equation obtained by setting the function equal to the \( y \)-coordinate of the horizontal line.

Learn how to solve the equation f(x) = -2 by analyzing the intersection points on a quadratic parabola graph. This detailed explanation includes steps to approximate x-values, mathematical concepts like graphing parabolas, and how to find exact solutions using the quadratic formula.

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