Question

The height h in feet if a projectile launched vertically upward from the top of a 96 ft tall tower when t=0 is given by h=96+80t-16t^2

Answer 1

4 ac - b²/4a

= 4 (-16)(110) - (16)²/ 4(-16) = 114

- b /2a = -(16)/2(-16) = 1/2 is the time it will take to reach the max height.

let t = 3 => h(t) = 110 + 16(3) - 16(3)² => 14

let t = 4 => h(t) = 110 + 16(4) - 16(4)² => -82

So the project around 3 and 4 seconds and the reason behind is that the positive h(t) leads to being above the ground and the negative h(t) value will indicate that the object is  below the ground which is not possible in any way.