Question: A quadratic function $y = f(x)$ is plotted on a graph and the vertex of the resulting parabola is $(-6, 3)$. What is the vertex of the function defined as $g(x) = -f(x - 4)$?
1. **State the problem:** We have a quadratic function $f(x)$ with vertex at $(-6, 3)$.
2. **Understand the transformation:** The function $g(x) = -f(x - 4)$ involves two transformations:
- Horizontal shift right by 4 units due to $(x - 4)$ inside the function.
- Reflection across the x-axis due to the negative sign in front of $f$.
3. **Apply horizontal shift:** The original vertex $(-6, 3)$ shifts right by 4 units:
$$x_{new} = -6 + 4 = -2$$
4. **Apply reflection:** The $y$-value of the vertex is reflected across the x-axis:
$$y_{new} = -3$$
5. **Final vertex:** Combining these results, the vertex of $g(x)$ is:
$$(-2, -3)$$
**Answer:** The vertex of $g(x) = -f(x - 4)$ is $(-2, -3)$.