Question

Write an equation for the translation of y=|x|. 2 units down.

Answer 1

B. Y = |x| - 2
when moving left or right...meaning moving horizontally.......the number is added inside the parenthesis. 

This one is moving up or down ....meaning moving horizontally........so the number is added outside the parenthesis. If it moves up then add(+)..........if it moves down then subtract(-). The formula used for horizontal shifts is, y=lXl + k
.Here k will become negative or remain positive based on the given data.

Now,
It's a horizontal shift, so we can eliminate C and D.
 It moves down so we will subtract and therefore we can eliminate A

so the answer is B.
 lets check our answer by using the formula

Y = lxl + k
moves 2 units down so our k = (-2)
Y = lxl + (-2)  [substitute k]
Y = lxl - 2

Answer 2

The answer should be B. y = |x| - 2. Hope I helped :)