Question

what is the equation of the new function?

Answer 1

The image g(x) of f(x) by shifting RIGHT h units is given by
g(x)=f(x-h)
Given f(x)=x^2, and h=-12 (LEFT makes h negative)
we get
g(x)=f(x-(-12))=f(x+12)=(x+12)^2   (if we do not expand expression)
=x^2+24x+144   (if we expand expression)