It is known that the quadratic function f (x) satisfies the conditions f (0) = 1 and f (x + 1) - f (x) = 2x. (1) find f (x); (2) find the maximum and minimum of F (x) in the interval [- 1, 1]

It is known that the quadratic function f (x) satisfies the conditions f (0) = 1 and f (x + 1) - f (x) = 2x. (1) find f (x); (2) find the maximum and minimum of F (x) in the interval [- 1, 1]

(1) Let f (x) = AX2 + BX + C, then f (x + 1) - f (x (x + 1) - f (x) = a (x + 1) 2 + B (x + 1) + C - (AX2 + BX + C) = 2aX + A + C, then f (x + 1) f (x + 1) is f (x + 1) f (x + 1) f (x + 1) f (x + 1) - f (f (x + 1) - f (x + 1) is a (x (x + 1) 2 (2) f (x) f (x) x (x) (2) x (x + 2) f (x) (x + 1) (x + 12) 12 + 12) 2 (12) 2 + 1 (12) 2 + 1 (12) 2 (12) 2 + 34) in the [- 1,12,12,12,12,12,12 (12] of the following [12,12] in [12,12 (12] we (12 (12 (12 (12 (12 (12 (12] max = f (- 1) = 3