Endgames: Q v P (a/h)

I'm not particularly good at Endgames, but now is as good a time as any to lock down some fundamentals.  The following occured in practice against a friend:

White didn't win this one, but they should have.  It is winning for white if the King is both inside the winning zone and has the move.  Some examples:

This is an example from Fundamental Chess Endings that I enjoyed: