Jon is launching rockets in an open field. the path of the rocket can be modeled by the quadratic function h(t) = -16t^2 + 96t, where h(t) is the height in feet any time t in seconds. after how many seconds will the rocket reach a height of 80 feet for the second time?

To solve the problem, substitute 80 feet to value of h(t). so given that
h(t) = -16t^2 + 96t

so
h(t) = -16t^2 + 96t = 80
 -16t^2 + 96t - 80 = 0
divide the whole equation with -16
(  -16t^2 + 96t - 80 = 0) 1/-16
t^2 - 6t + 5 = 0
factor the quadratic equation
( t - 5 ) ( t - 1 ) = 0
t = 5
t = 1
so the answer would be 5 s, because it the rocket will reach the 80 ft for the first time at 1 s