Given the quadratic function f (x) = AX2 + BX + C, if f (x) + F (x + 1) = 2x2-2x + 13 (1), find the analytic expression of function f (x); (2) draw the image of the function; (3) find the maximum value of function f (x) when x ∈ [T, 5]

Given the quadratic function f (x) = AX2 + BX + C, if f (x) + F (x + 1) = 2x2-2x + 13 (1), find the analytic expression of function f (x); (2) draw the image of the function; (3) find the maximum value of function f (x) when x ∈ [T, 5]

(1) F (x) + F (x + 1) = AX2 + BX + C + a (x + 1) 2 + B (x + 1) + C = 2ax2 + (2a + 2b) x + A + B + 2C ∫ f (x) + F (x + 1) = 2x2-2x + 13 ∫ 2A = 22a + 2B = - 2A + B + 2C = 13 ∫ a = 1b = - 2C = 7 ∫ f (x) = x2-2x + 7 (2) the function is that the axis of symmetry is x = 1, the vertex is (1,6), and has no relation with the X axis