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Question

Compared to the graph of f(x)=x², the graph of g(x)=(x+3)²-2 is the result of translating f(x)?

Answer 1

^{For any Core function f(x)}

any translation in the form g(x) = f(x+a) will move the function a units to the left. If in the form g(x) = f(x-a) one will move a units to the right.

for any translation in the form of g(x) = f(x) + a, the function f(x) is moved a units up. If in the form f(x) - a, one would move the core function a units down

Thus for the function g(x) = (x+3)² - 2, you have a combination of transformations. Essentially you move the core function f(x) = x²: 3 units to the left and down two units down from its original vertex of (0,0)