Question: A quadratic function $y = f(x)$ is plotted on a graph and the vertex of the resulting parabola is $(-4, -6)$. What is the vertex of the function defined as $g(x) = f(x) + 3$?

1. **State the problem:** We have a quadratic function $y = f(x)$ with vertex at $(-4, -6)$. We define a new function $g(x) = f(x) + 3$ and want to find the vertex of $g(x)$. 2. **Recall the vertex form and transformation rule:** The vertex of $f(x)$ is at $(-4, -6)$. Adding a constant $+3$ to the function shifts the graph vertically upward by 3 units. 3. **Apply the vertical shift:** The $x$-coordinate of the vertex remains the same because horizontal position does not change. 4. **Calculate the new $y$-coordinate:** $$-6 + 3 = -3$$ 5. **Conclusion:** The vertex of $g(x)$ is at $(-4, -3)$. This means the parabola moves up 3 units but stays horizontally aligned at $x = -4$.