What is the gravitational potential energy?

it occurs continually from start to finish, increasing or decreasing as reequired

Your maximum gravitational potential energy will occur at the maximum height of the ball. As it falls the potential energy will be converted to kinetic energy until right before it hits the ground and the potential energy will have all been converted to kinetic energy (and it'll be moving at its max speed in the vertical direction).

When you throw it up kinetic energy gets converted to potential energy until it is at its peak (which is why is comes to a stop in the vertical direction).

In the middle between its peak and the ground it will have some of both.

Hope that helps!

Gravitational Potenial energy is a form of stationary energy. It's when something has the Potenial to fall, but it's not falling. For example, a book sitting on a shelf has gravitational potential energy, or a poster on a wall has gravitational potential energy. Your example doesn't have this kind, it's just basic kinetic to potential, when it's on the ground. The MOST gravitational potential, however, is when it's highest in the air, but it's still slightly moving, so it's not full gravitational potential energy, I hoped this helps xx

Energy is a relative concept.  For example imagine a 1000kg car driving at 10 m/s, you could say it has E=1/2mv^2 = 50,000 Joules of kinetic energy.  However if another car is driving towards it, at the same speed, from it's perspective, the car coming towards it has a relative speed of 20m/s and therefore has 200,000 Joules of kinetic energy.

Likewise, if you are standing on the surface of the earth, you have gravitational potential energy that is different depending on which point in the gravitational well you are comparing it too.  For example, if your point of reference is the surface of the earth, and your object is on the surface, it has E=mgh = 0 J of potential gravitational energy.  But if your point of reference is the center of the earth, then the potential energy is E=mgh = m*9.8*6,300,000.