Let f (x) = x ^ 2-2ax + 1 (a is a real number) be g (a) when - 2 ≤ x ≤ 1 Find g (a) expression, monotone interval, range

Let f (x) = x ^ 2-2ax + 1 (a is a real number) be g (a) when - 2 ≤ x ≤ 1 Find g (a) expression, monotone interval, range

F (x) = x & # 178; - 2aX + 1 = (x-a) &# 178; + 1-A & # 178; the opening of the image is upward, and the axis of symmetry x = a
① When a ≤ - 2, f (x) gets the minimum at x = - 2, G (a) = f (- 2) = 5 + 4a
② When - 2 < a < 1, the minimum value of F (x) is obtained at x = a, G (a) = f (a) = 1-A & # 178;
③ When a ≥ 1, the minimum value of F (x) at x = a is g (a) = f (1) = 2-2a
5+4a a≤-2
So g (a) = 1-A & # 178; - 2 < a < 1
2-2a a≥1