Answer
$8$ feet
Work Step by Step
We use the $x$-coordinates of the points where the entrance meets the ground to find the width of the entrance at ground level. At ground level, $y=0$. So we substitute $0$ for $y$ and solve for $x$:
$$\begin{align*}
y&=-\frac{1}{2}(x+4)(x-4)&&\text{Write equation.}\\
0&=-\frac{1}{2}(x+4)(x-4)&&\text{Substitute }0\text{ for }y\\
0&=(x+4)(x-4)&&\text{Multiply each side by }-2\\
x+4&=0\text{ or }x-4=0&&\text{Zero-Product Property.}\\
x&=-4\text{ or }x=4&&\text{Solve for }x.
\end{align*}$$ The width of the entrance is the distance between the $x$-coordinates, $-4$ and $4$. So the width of the entrance at ground floor is $|-4-4|=8$ feet.
