Question

The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?

g(x) = (x − 7)2 − 3
g(x) = (x + 7)2 − 3
g(x) = (x − 3)2 − 7
g(x) = (x − 3)2 + 7

Answer 1

g(x) = (x + 7)^2 − 3

Reason: left 7 shifts x to x+7 (inside), down 3 subtracts 3 (outside). The vertex moves from (0,0) to (−7, −3).