A) when does the ball reach its maximum height?

You want to solve this equation for the maximum value. There are a number of ways to do this. The easiest by far, if you've taken calculus is to take its derivative and set it equal to zero, and solve for t. Another option is to set this equation equal to zero and find the x-intercepts. Knowing that the maximum will be right in the middle of the two you can take the average two points.