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The question asks for the coordinates of the x-intercepts for the function \( g(x) = -x^2 + 4 \).

To find the x-intercepts, we need to set \( g(x) = 0 \) because x-intercepts occur when the output of the function (y-value) is zero.

### Step 1: Set the equation to 0
\[
0 = -x^2 + 4
\]

### Step 2: Solve for \( x \)
\[
x^2 = 4
\]

Now, take the square root of both sides:
\[
x = \pm 2
\]

### Step 3: Find the coordinates
Thus, the x-intercepts are at \( x = -2 \) and \( x = 2 \). The corresponding coordinates are \( (-2, 0) \) and \( (2, 0) \).

### Conclusion:
The correct answer is **Option 2**, which gives the x-intercepts \( (-2, 0) \) and \( (2, 0) \).

Do you want more details or have any questions?

Here are 5 related questions to expand on this:
1. What are the steps to find the y-intercept of a quadratic function?
2. How do the signs of the coefficients in a quadratic function affect its graph?
3. How would you determine the vertex of \( g(x) = -x^2 + 4 \)?
4. What is the axis of symmetry for the function \( g(x) = -x^2 + 4 \)?
5. How does the graph of \( g(x) = -x^2 + 4 \) differ from \( g(x) = x^2 - 4 \)?

**Tip:** When finding x-intercepts of quadratic functions, always set \( g(x) = 0 \) and solve for \( x \).

What are the coordinates of the x-intercept(s) for the function g(x) = -x^2 + 4?

This lesson demonstrates how to find the x-intercepts of the quadratic function g(x) = -x^2 + 4. Students will learn the process of setting g(x) to 0, solving the equation, and interpreting the results graphically. Suitable for students in Grades 8-10.

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