If a rock is thrown in the air, when will it have the greatest potential energy?

Question

I'm thinking the answer is at the highest point because it slows and is just about to head down and accelerate, am I right?

Answer 1

Yes, you are correct. The greatest potential energy of the rock will be at the highest point of its trajectory when it is just about to start descending. At that point, the rock has gained the maximum height and its velocity becomes zero before it starts accelerating downward due to gravity.