The curve S has equation y = f(x) where f(x) = x^2 The curve T has equation y = g(x) where g(x) = 2x^2 – 12x + 13

By writing g(x) in the form a(x – b)^2 – c, where a, b and c are constants,

describe fully a series of transformations that map the curve S onto the curve T.​