Question

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6?

left 3 units, down 3 units
right 3 units, down 3 units
left 6 units, down 1 unit
right 6 units, down 1 unit

Answer 1

Complete the square: x^2 − 6x + 6 = (x − 3)^2 − 3. So g(x) = f(x − 3) − 3, which is f shifted right 3 units and down 3 units.