I don’t understand this still

Question

Please walk me through all the steps

The quadratic function g(x) = (x+3)^2 - 2is given below. The function h(x) is a transformation of g(x). Write an equation for h(x) in terms of g(x).

(x, g(x)) values are (-4,-1), (-3,-2), (-2,-1), (-1,2), (0,7)

(x, h(x)) values are (0,2), (1,1), (2,2), (3,5), (4,10)

Answer 1

In looking at the data provided, we can see that h(x) is g(x), but shifted right by 4 and up by 3. To write h(x) in terms of g(x), we simply substitute in those transformations, h(x) = g(x-4) + 3.

Answer 2

f(x) = x²

then

g(x) = (x + 3)² -2 is f(x) shifted 3 to the left and down 2

h(x) is g(x) shifted 4 to the right (e.g., x = -4 becomes 0) and up 3 up (e.g. g(x) = -1 become 2

h(x) = (x + 3 - 4)² - 2 + 3

h(x) = (x - 1)² + 1