Given the function FX = x & sup2; - 2aX + 3 (1 ≤ x ≤ 3), find the minimum value H (a) of function FX and write the monotone interval of function H (a)

Given the function FX = x & sup2; - 2aX + 3 (1 ≤ x ≤ 3), find the minimum value H (a) of function FX and write the monotone interval of function H (a)

F (x) = (x-a) ^ 2 + 3-A ^ 2, parabolic opening upward, axis of symmetry x = a
1) If A3, then f (x) is a decreasing function on [1,3], so min = f (3) = 12-6a,
3) If 1