What does the equation y = a(x - h)2 + k, a ≠ 0 represent?

Answer 1

you know what y=ax^2 is, right?

Now shift it by (h,k)

Answer 2

how do you shift y=ax^2 by (h,k)

Answer 3

replace y by (y-k) and x by (x-h)

Better review your text where it talks about translation of functions.