Atee box is 48 feet above its fairway.

0 = -16t ^ 2 + 32t + 48
 Part A: 
 Factoring we have:
 0 = -16 (t ^ 2 - 2t + -3)
 0 = (t ^ 2 - 2t + -3)
 0 = (t + 1) * (t-3)
 t> 0
 t-3 = 0
 t = 3
 
 The ball is in the air for 3 s.

 Part B:
 h (t) = - 16t ^ 2 + 32t + 48
 We evaluate for t = 1
 h (1) = - 16 * (1) ^ 2 + 32 * (1) + 48
 h (1) = 64
 
 The height of the ball at 1 second is: 
 h (1) = 64 feet

 Part C:
 We derive the equation and we equate to zero:
 h '(t) = - 32t + 32
 0 = -32t + 32
 32t = 32
 t = 1
 h '' (t) = - 32 <0 (t = 1 is a maximum)
  
 Yes, The ball at its maximum height at t = 1 second.