Question 1103985
A ball is thrown vertically upward from the top of a building 96 feet tall with an initial velocity of 80 feet per second. The distance, s (in feet), of the ball from the ground after t seconds is given by the function:
��(��) = 96 + 80�� − 16��^2
seeing this graphically is helpful
{{{ graph( 300, 200, -6, 10, -50, 220, -16x^2+80x+96, 196) }}}
a.) How long does it take for the ball to reach its
highest point?
This is a quadratic equation, max occurs on the axis of symmetry x=-b/(2a)
t = {{{(-80)/(2*-16)}})
t = {{{(-80/(-32)}}}
t = 2.5 seconds
:
b.) What is the maximum height the ball reaches? 
Replace t with 2.5 to find s
s = -16(2.5^2) + 80(2.5) + 96
s = -16(6.25 )+ 200 + 96
s = -100 + 296
s = 196 ft is max height, green line