To plot the modulus of a function reflect any negative part of f(x) in the x axis.

In your example reflect the portion between in the y axis

is moving the graph by a on the y axis.It can go negative if a is sufficiently negative

is a translation of f|x| on the x axis.

can be +ve or -ve depending on the value of a.

For example

edit: for your example see these wolfram alpha plots