Question

Which statement describes the translation of y = –1/2 (x – 2)2 – 2 from standard position?

Answer 1

well (h,k) is your vertex. a is your slope. It is in y=a(x-h)+k
So the given equation would negate the graph opening it downwards rather than upwards.
The graph would look twice as wide as the normal one. The vertex would be shifted two units to the right and two units down.

Answer 2

"which statement" indicates that there is a choice of options

Answer 3

i'm not sure whether you mean -(1/2 X (x-2) X 2) -2 or -1/2(x-2)^2 -2. but anyway, for the first one the 1/2 qnd the two cancel leaving -(x-2) -2
expanding the brackets gives -x+2-2 =-x so this is a reflection in the x axis of the line y=x

if its the second one the it is first a translation of -2 in the y direction and then a stretch of scale factor a half in the y direction and then a translation of 2 in the x direction of the curve y=x^2

hope that helps