y = -16x^2 + 105x + 12
Time to reach max ht = -105 / [ 2 * -16] = 105/32 sec
Put this into the function to find the max height =
-16 (105/32)^2 + 105(105/32) + 12 = 184.27 ft
And the time it takes to hit the ground =
-16x^2 + 105x + 12 = 0
( -105 ±√ [ 105^2 - 4(-16)(12) ] ) / [ 2 (-16)]
( -105 ±√ 11793 ) / -32 take the negative sign
( -105 - √11793 ) / -32 ≈ 6.67 sec