#### Answer

a. maximum height $ 55\ ft$, $x= 100\ ft$
b. $204.9\ ft$

#### Work Step by Step

a. With the given equation $f(x) = -0.005x^2 + x + 5$, we have $a=-0.005, b=1$ and the maximum height happens at $x=-\frac{b}{2a}=-\frac{1}{-0.01}=100\ ft$ and the maximum height is
$f(100)=-0.005(100)^2 + (100) + 5=55\ ft$
b. The travel distance can be found by letting $f(x)=0$:
$ -0.005x^2 + x + 5=0$
which can be solved using a formula or graphically to get $x\approx204.9\ ft$ as shown in the figure.