PLS PLS HELPPP WITH MATHHH, EXPLANTION NEEDED!!

Equation: y= a(x-h)^2 + k

translations:

y= x^2 (opens up)
y= -x^2 (opens down)
(in your case, it would open down since it’s -)

vertical shifts (k)-
y= x^2 + k (shifting k units up)
y= x^2 - k (shifting k units down)
(in this case, it would shift 6 units down)

horizontal shifts (h)-
this doesn’t apply to your equation since there’s no h but I hope this will help future questions similar to this one.
**take note that the equation is (x-h), so for ex... if h= -3, (x-(-3))= (x+3). negative plus negative equals positive. if h = 2, (x-2)**

y= (x^2 - #) [shifting # units to the right]
y= (x^2 + #) [shift # units to the left]

variables h & k also will determine its vertex point!

h affects x
k affects y

since there’s no specific h, it’ll automatically be 0, since there’s no translation to h, it’ll stay there. since your equation’s k= -6, it’ll shift 6 units down.

hope this helps. you got this! :)