Answer
a. maximum height at $x=20\ yards$ with $f(20)=16\ ft$
b. $6\ ft$
c. $ 45.3\ yards$
d. See graph
Work Step by Step
a. Given
$f(x)=-0.025x^2+x+6=-0.025(x^2-40x+400)+10+6=-0.025(x-20)^2+16$
we can identify a maximum height at $x=20\ yard$ with $f(20)=16\ ft$
b. The initial height is given at $x=0$ with $f(0)=6\ ft$
c. Let $f(x)=0$; we have $-0.025(x-20)^2+16=0$, which gives $x=20\pm\sqrt {640}$ and $x\approx45.3\ yard$ (discard negative answer).
d. See the graph of the function.
