Step 1 :The function given is a quadratic function. The maximum height of the ball is the maximum value of the function, which occurs at the vertex of the parabola.
Step 2 :The x-coordinate of the vertex of a parabola given by the equation \(y = ax^2 + bx + c\) is \(-b/2a\).
Step 3 :In this case, \(a = -16\) and \(b = 48\), so the time at which the maximum height is reached is \(-b/2a = -48/(-32) = 1.5\) seconds.
Step 4 :We can substitute this value into the function to find the maximum height.
Step 5 :The maximum height that the ball reaches is \(\boxed{64}\).