1. **State the problem:** We are given the function $h(x) = (x - 4)^2$ and the parent function $f(x) = x^2$. We need to identify the transformations applied to $f(x)$ to get $h(x)$. 2. **Recall the parent function:** The parent function $f(x) = x^2$ is a parabola with vertex at $(0,0)$ opening upwards. 3. **Analyze the given function:** The function $h(x) = (x - 4)^2$ can be seen as a horizontal translation of $f(x)$. 4. **Transformation rule:** For a function $g(x) = (x - h)^2$, the graph of $f(x) = x^2$ is translated horizontally by $h$ units. If $h$ is positive, the translation is to the right; if negative, to the left. 5. **Apply the rule:** Here, $h = 4$, so the graph of $f(x)$ is translated 4 units to the right. 6. **Vertex of $h(x)$:** The vertex moves from $(0,0)$ to $(4,0)$. 7. **Check reflection and vertical translation:** There is no negative sign outside the square, so no reflection. There is no added or subtracted constant outside the square, so no vertical translation. 8. **Summary:** The function $h(x) = (x - 4)^2$ is the graph of $f(x) = x^2$ translated 4 units to the right. The vertex is at $(4,0)$, and the parabola opens upwards. **Note:** The user's statement about the vertex at $(-4,0)$ and translation down 4 is incorrect based on the function given. Final answer: The graph of $f(x) = x^2$ is translated 4 units to the right to get $h(x) = (x - 4)^2$. The vertex is at $(4,0)$, no reflection or vertical translation applied.