The problem asks us to graph the function $g(x) = (x+4)^2$.

1. Problem Description

The problem asks us to graph the function $g(x) = (x+4)^2$.

2. Solution Steps

The given function is a quadratic function in the form $g(x) = (x-h)^2 + k$, where the vertex of the parabola is at the point $(h, k)$. In this case, we can rewrite the given function as $g(x) = (x - (-4))^2 + 0$.

Thus, $h = -4$ and $k = 0$. The vertex of the parabola is at $(-4, 0)$.

The basic parabola $y = x^2$ opens upwards.

The function $g(x) = (x+4)^2$ is a horizontal shift of the basic parabola $y = x^2$ by 4 units to the left.

To graph the parabola, we can find a few points.

When $x = -3$, $g(-3) = (-3+4)^2 = (1)^2 = 1$.

When $x = -5$, $g(-5) = (-5+4)^2 = (-1)^2 = 1$.

When $x = -2$, $g(-2) = (-2+4)^2 = (2)^2 = 4$.

When $x = -6$, $g(-6) = (-6+4)^2 = (-2)^2 = 4$.

When $x = -1$, $g(-1) = (-1+4)^2 = (3)^2 = 9$.

When $x = -7$, $g(-7) = (-7+4)^2 = (-3)^2 = 9$.

So, some points on the graph are $(-4, 0)$, $(-3, 1)$, $(-5, 1)$, $(-2, 4)$, $(-6, 4)$, $(-1, 9)$, and $(-7, 9)$.

The graph is a parabola with vertex at $(-4, 0)$ opening upwards.

3. Final Answer

$g(x) = (x+4)^2$