Answer
$77.8$ feet; Graph (b)
Work Step by Step
In order to determine the maximum distance, we solve the equation $f(x)=0$ using the Quadratic Formula:
$$\begin{align*}
-0.01x^2+0.7x+6.1&=0\\
0.01x^2-0.7x-6.1&=0\\
x&=\dfrac{-(-0.7)\pm\sqrt{(-0.7)^2-4(0.01)(-6.1)}}{2(0.01)}\\
&\approx\dfrac{0.7\pm 0.8567}{2(0.01)}\\
x_1&\approx -7.8\\
x_2&\approx 77.8.
\end{align*}$$
Because $x\geq 0$ only the solution $x=77.8$ fits.
The graph that shows the shot's path is Graph (b).
