The height h in feet of a projectile launched vertically upward from the top of a 96 foot tall bridge is givem by h=90+16t-16t^2 where t is time in seconds. what is the maximum height an how long will it tale the projectile to strike the ground?

Hi!

h(t)= -16t^2+16t+90 
h(t) = -16(t^2 - t) + 90 
h(t) = -16(t^2 - t + (1/2)^2) + 90 + 4 
h(t) = -16(t - 1/2)^2 + 94 
vertex at(1/2 , 94) , since a = -16 < 0 , the parabola opens down, which makes the vertex. the global maximum, so: 
Max at(1/2 , 94) 
object hits the ground at h = 0, then: 
-16(t - 1/2)^2 + 94 = 0 
(t - 1/2)^2 = 94/16 = 47/8 
t - 1/2 = ± √(47/8) 
t = 1/2 ± √(47/8) 
t = -1.9 , 2.9 => reject t = -1.9 
t = 2.9 sec => time it takes for the projectile to hit the ground