Peter R. answered 10/04/22
Experienced Instructor in Prealgebra, Algebra I and II, SAT/ACT Math.
Moving the function to the left 8 units is counter-intuitive; you have to add 8 within the function: f(x) = (x + 8)1/2.
Then moving it down 12 is straightforward; f(x) = (x+8)1/2-12. Check on the Desmos graphing calculator website.