When a ball is thrown in the air and is modeled with a quadratic function, we can determine the time to reach the maximum height is differentiate the function in terms of x and t and equate to zero. In this case, we can plot the function as a parabola that is opening downwards. The vertex is the point where the ball reaches the top. The x-coordinate is the time and the y-coordinate is the height of the ball. The answer is the x-coordinate of the vertex.