1. The problem asks how the graph of $g(x) = (x + 7)^2 + 4$ is related to the graph of $f(x) = x^2$. 2. The base function is $f(x) = x^2$, which is a parabola opening upward with vertex at the origin $(0,0)$. 3. The function $g(x) = (x + 7)^2 + 4$ can be seen as a transformation of $f(x)$. 4. The formula for horizontal and vertical shifts is: $$g(x) = f(x - h) + k$$ where $h$ is the horizontal shift and $k$ is the vertical shift. 5. In $g(x) = (x + 7)^2 + 4$, rewrite $x + 7$ as $x - (-7)$, so $h = -7$ and $k = 4$. 6. This means the graph of $f(x)$ is shifted left by 7 units (because $h = -7$) and up by 4 units (because $k = 4$). 7. The vertex of $g(x)$ is at $(-7, 4)$. 8. The shape of the parabola remains the same (opening upward), only its position changes. Final answer: The graph of $g(x) = (x + 7)^2 + 4$ is the graph of $f(x) = x^2$ shifted left 7 units and up 4 units.