1. The problem asks how the graph of $g(x) = (x + 6)^2 + 1$ is related to the graph of $f(x) = x^2$. 2. The base function is $f(x) = x^2$, which is a parabola with vertex at $(0,0)$. 3. The function $g(x) = (x + 6)^2 + 1$ can be seen as a transformation of $f(x)$. 4. The term $(x + 6)^2$ shifts the graph horizontally. Since it is $x + 6$, the graph shifts left by 6 units. 5. The $+1$ outside the squared term shifts the graph vertically up by 1 unit. 6. Therefore, the graph of $g(x)$ is the graph of $f(x)$ shifted left 6 units and up 1 unit. 7. The vertex of $g(x)$ is at $(-6, 1)$. 8. The shape of the parabola remains the same (opens upward). Final answer: The graph of $g(x) = (x + 6)^2 + 1$ is the graph of $f(x) = x^2$ shifted left 6 units and up 1 unit.