Given that the function f (x) = 4x ^ 2-4ax + A ^ 2-2a + 2 has the minimum value 3 in the interval [0,2], find the value of A Don't Scribble if you can't do it, so as not to influence others to help me solve the problem

Given that the function f (x) = 4x ^ 2-4ax + A ^ 2-2a + 2 has the minimum value 3 in the interval [0,2], find the value of A Don't Scribble if you can't do it, so as not to influence others to help me solve the problem

Obviously, a ≠ 0, because the coefficient of the quadratic term is 4 > 0, the opening of the function image (parabola) is upward. If 3 is the minimum value of the function, it is obviously not in line with the meaning of the problem. Therefore, consider two cases where the function is an increasing function or a decreasing function in the interval [0,2], that is, f (0) = 3 or F (2) = 3, a = 1 ± 2 under the root sign or a = 5 ± 10 under the root sign, respectively