Answer
$f(x)=-|x|-12$
Work Step by Step
Since the shape of the graph is a $f(x) = |x|$ we will start with that function:
$f(x)=|x|$
The transformation is 12 units up. Up and down transformations are added to the right side. Up is positive and down is negative.
$f(x)=|x|+12$
The reflection is across the x-axis. X-axis reflections mean multiplying the right side by -1
$f(x)=-|x|-12$
