Question

Which of these is true about kinetic energy but not necessarily true about potential energy

Answer 1

Kinetic energy is never negative, but potential energy can be.

Potential energy depends on height above some reference level,
and you can pick any level you want as the reference.  So, if the
object is below the reference level you pick, then its potential
energy relative to your reference level is negative. 

What that means is:  You have to lift it / do work on it / give it more
energy than it has now ... in order to move it to the reference level.

(That's exactly the situation with electrons bound to an atom.  Their
energy is considered negative, because we have to do work and
give them more energy to rip them away from the atom.)
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Regarding the other choices:

-- Kinetic energy is scalar ... Yes.  So is potential energy.

-- Kinetic energy increases with height ...
   No. It doesn't, but potential energy does.

-- Kinetic energy depends on position ...
   No. It doesn't, but potential energy does.