The height of the object at any given time t is given by the function h(t) = -t^2 + 6t + 10. To find the maximum height, we need to find the vertex of the parabola described by this function.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the y-coordinate of the vertex.
In this case, a = -1, b = 6, and c = 10, so we have:
t = -b/2a = -6/(-2) = 3
To find the maximum height, we need to evaluate h(3):
h(3) = -(3)^2 + 6(3) + 10 = 9 + 18 + 10 = 37
Therefore, the maximum height of the object is 37 units, which occurs when t = 3 seconds.