No, you don't.
You loose a 1st level spell (mage armor)
and
a first level spell from a different arcane casting class, of the spell level adjustment of the metamagic feat: +1.
(Note the word adjustment )
An Empowered fireball would require a 3rd level spell( fireball) and a 2nd level spell (Empower)
A Maximized Fireball would require a 3rd level spell (fireball) and another 3rd level spell (Maximize).
You are correct, the example in the book makes it clear
To empower a spell, for example, you would have to spend a 2nd level or higher spell.
Interestingly enough you can't use this ability to augment a spell already affected by a metamagic feat. So you can only apply 1 metamagic feat to a spell at a time.