As shown in the figure, it is known that the parabola y = 1 / 2x ^ 2 + MX + n (n ≠ 0) intersects the straight line y = x at two points a and B, intersects the Y axis at point C, OA = ob, and AC ‖ X axis As shown in the figure, it is known that the parabola y = 1 / 2x ^ 2 + MX + n (n ≠ 0) intersects with the straight line y = x at two points a and B, intersects with the Y axis at point C, OA = ob, and AC ‖ X axis (1) finds the functional relationship corresponding to the parabola (2) let D and E be two moving points on the line AB different from a and B (point E is above d). De = √ 2, make parallel lines of Y axis respectively through D and E, intersect the parabola and FG, if the abscissa of point D is x, the area of the quadrilateral degf is y, and, Try to find the relationship between Y and X and the value range of X

As shown in the figure, it is known that the parabola y = 1 / 2x ^ 2 + MX + n (n ≠ 0) intersects the straight line y = x at two points a and B, intersects the Y axis at point C, OA = ob, and AC ‖ X axis As shown in the figure, it is known that the parabola y = 1 / 2x ^ 2 + MX + n (n ≠ 0) intersects with the straight line y = x at two points a and B, intersects with the Y axis at point C, OA = ob, and AC ‖ X axis (1) finds the functional relationship corresponding to the parabola (2) let D and E be two moving points on the line AB different from a and B (point E is above d). De = √ 2, make parallel lines of Y axis respectively through D and E, intersect the parabola and FG, if the abscissa of point D is x, the area of the quadrilateral degf is y, and, Try to find the relationship between Y and X and the value range of X

According to the analytic expression of the function, C (0, n) ∵ AC / / X axis ∥ a (- 2m, n) ∥ n = - 2m ∵ OA = ob ∥ B (2m, 2m) is substituted into the analytic expression to get (1 / 2) (2m) ^ 2 + m * (2m) - 2m = 2m ∥ 4m ^ 2 - 4m = 0 ∥ M = 1 or M = 0 (when m = 0, n = 0 does not satisfy the problem) ∥ M = 1 ∥ the parabolic analytic expression is y = 0.5x ^ 2 + X-2, let e (x + T, x + T) ∥ de = √ 2