Solve for x. Assume that lines which appear tangent are tangent.

For this case we have the following function:
 w (x) = - 5 (x-8) (x + 4)
 Rewriting we have:
 w (x) = - 5 (x ^ 2 + 4x - 8x - 32)
 w (x) = - 5x ^ 2 - 20x + 40x + 160
 w (x) = - 5x ^ 2 + 20x + 160
 Then, deriving we have:
 w '(x) = - 10x + 20
 We equal zero and clear x:
 0 = -10x + 20
 10x = 20
 x = 20/10
 x = 2 seconds
 Substituting values:
 w (2) = - 5 (2-8) (2 + 4)
 w (2) = - 5 (-6) (6)
 w (2) = 180 meters
 
 The maximum height that the stone will reach is:
 w (2) = 180 meters