Gravitation Potential Energy -- Questions about calculating the sign of GPE

[Quantum Psi Inverted]

Homework Statement

When does one use mgh0-mghf, and when does one use mghf-mg0? Is all gravitation potential energy necessarily negative?

Relevant Equations

E=(m/2)(vf^2-v0^2)+mg(hf-h0)
PE=mg(h0-hf)

I believe that this is due to context of application, but now, I'm starting to doubt myself. For example, a helicopter lifting itself has positive PE change. I really don't intuitively understand how this works. Can someone kindly explain this to me?

 

[PeroK]

Relative to the ground, GPE (gravitational potential energy) is always positive. A change in GPE can be positve or negative.

 

[haruspex]

Homework Statement: When does one use mgh0-mghf, and when does one use mghf-mg0? Is all gravitation potential energy necessarily negative?

Those are two different questions.

Assuming the 0 and f are supposed to indicate initial and final heights, mghf-mg0 gives you the (signed) change in PE. mgh0-mghf gives you the loss in PE, obviously.

All "potentials" are in principle relative, i.e. it is up to you to choose where the zero potential is. However, a convention commonly used, both for GPE and electrostatic, is that the potential at infinity is zero. That makes all other GPEs negative.
At a greater height, the potential is less negative, so is greater than at a lower height.