Question 966364
a stone is thrown upward from a bridge. the stones height s(t) in ft, above the water t seconds after the stone is thrown is given by the function s(t)=-16t^2+32t+256. 
a. find the max height of stone. 
s(t)=-16t^2+32t+256
complete the square:
s(t)=-16(t^2-2t+1)+16+256
=-16(t-1)^2+272
This is an equation of a parabola that opens downward with vertex at (1, 272)
stone reaches maximum height of 272 ft, 1 sec after it is thrown.
..
b. find the time it takes the stone to hit the water?
when stone hits the water, s(t), height=0
-16t^2+32t+256=0
t^2-2t-16=0
use quadratic formula to solve for t
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1, b=-2, c=-16
ans:
t=5.12 sec