Step-by-step explanation:
Recall that for a quadratic equation y = ax² + bx + c in the X-Y plane, the x-location of the vertex (i.e maximum or minimum point) is given by
x @vertex = -b/2a
in this case your quadratic equation is
h = 4 + 20t - 5t² (rearranging in the form y = ax² + bx + c )
h = - 5t² + 20t + 4
hence a= -5, b = 20 and c = 4
applying the formula for vertex
t @ vertex = -b /2a = -(20) / (2)(-5) = -20/-10 = 2
therefore t = 2
