An object is launched upward with an initial velocity of 64 feet per second from a platform 80 feet high. write a model for the object? how many seconds until the maximum height is reached? what will be the maximum height? how many seconds until the object hits the ground

Using one of the equations for costant acceleration 
s = ut + 0.5gt^2 + 80
s = 64t - 16t^2  + 80

s = -16t^2 + 64t + 80
   = -16[ t^2 - 4t) + 80
   = -16 ( t - 2)^2 + 64 + 80
   = -16(t - 2)^2 + 144
Time to maximum height = 2 seconds
Maximum height = 144 ft

Displacement when it hits the ground  = -80 so

-80 = -16t^2 + 64t + 80

solve for t 

t = 5.74 seconds

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.