Answer
$55.3$ feet; graph (a)
Work Step by Step
In order to determine the maximum distance, we solve the equation $f(x)=0$ using the Quadratic Formula:
$$\begin{align*}
-0.04x^2+2.1x+6.1&=0\\
0.04x^2-2.1x-6.1&=0\\
x&=\dfrac{-(-2.1)\pm\sqrt{(-2.1)^2-4(0.04)(-6.1)}}{2(0.04)}\\
&\approx\dfrac{2.1\pm 2.321}{2(0.04)}\\
x_1&\approx -2.8\\
x_2&\approx 55.3.
\end{align*}$$
Because $x\geq 0$ only the solution $x=55.3$ fits.
The graph that shows the shot's path is Graph (a).
