Let f (x) = AX2 + BX + C have the maximum and minimum values of M and m respectively in the interval [- 2,2], and set a = {x ﹤ f (x) = x} (1) if a = {1,2} (2) if a = {2} and a ＞ 0, let g (a) = M-M and find the expression of G (a)

Let f (x) = AX2 + BX + C have the maximum and minimum values of M and m respectively in the interval [- 2,2], and set a = {x ﹤ f (x) = x} (1) if a = {1,2} (2) if a = {2} and a ＞ 0, let g (a) = M-M and find the expression of G (a)

The original formula is AX2 + BX + C-F (x) = 0
In a, f (x) = X
Just put it in

The quadratic function y = 1 / 2 (X-H) ^ 2 is known if and only if 2

Reference:
If x = 2, y = x, then 1 / 2 (2-h) ^ 2 = 2, the solution is h = 0 or 4. If h = 0, x = 3, then 1 / 2 × 3 ^ 2 ≮ 3 does not conform to the meaning of the problem ≮ H = 4
Suppose x = m, y = x, then 1 / 2 (M-4) ^ 2 = M solution is m = 2 (rounding off) or M = 8
∴h=4,m=8
Sketch of quadratic function y = 1 / 2 (x-4) ^ 2