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The question asks for the solutions of the function \( g(x) = -x^4 + 6x^2 - 8 \) at certain points, based on the provided graph.

### Steps to Solve:
1. **Identify where \( g(x) = -2 \)** on the graph:
   - We need to find the **x-values** where the function reaches the value of **-2** on the y-axis (i.e., \( g(x) = -2 \)).
   - This corresponds to the points where the horizontal line \( y = -2 \) intersects the curve.

2. **Interpreting the Graph:**
   - From the graph, the curve intersects \( y = -2 \) at two points:
     - One near **x = -2**.
     - One near **x = 2**.

3. **Checking the Options:**
   - From the possible choices:
     - The correct pair of solutions appears to be **\( x = -2 \) and \( x = 2 \)**.

### **Answer:**
- The correct option is:
  **\( x = -2 \) and \( x = 2 \)**.

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Here are 5 related questions for more practice:
1. What is the degree of the polynomial \( g(x) = -x^4 + 6x^2 - 8 \)?
2. How do the roots of a polynomial relate to its graph's x-intercepts?
3. What happens to the graph of a function when the leading coefficient is negative?
4. How do you determine the maximum or minimum points of a polynomial function?
5. What does the multiplicity of a root tell us about the shape of the graph at that root?

**Tip:** When solving for roots or specific values of a function, look carefully at the intersections of the graph with horizontal lines!

The graph of the function g(x) = -x^4 + 6x^2 - 8 is shown. Which are the solutions of g(x) = -2?

Discover how to solve the function g(x) = -x^4 + 6x^2 - 8 at y = -2 using graphical interpretation. Learn to identify points of intersection and the corresponding x-values. Ideal for Grades 9-11 students.

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