Question

Can anyone explain: The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x) = x²?

Answer 1

f(x+8) = (x+8)^2 this translates the graph of x^2 eight units to the left....
f(x+8) + 2 = (x+8)^2 + 2 and this moves it 2 units upward.

so, \(\large g(x)=f(x+8)+2=(x+8)^2 + 2 \)

you can expand and the binomial and get it in \(\large g(x)=ax^2+bx+c \) form if you want but the previous shows the transformations.....