If the parabola y = - x ^ 2 + 2 (k-1) x + 2k-k ^ 2 passes through the origin and opens downward, find: 1 the analytic expression of quadratic function 2. The area of triangle formed by intersection A.B and vertex C of X axis

If the parabola y = - x ^ 2 + 2 (k-1) x + 2k-k ^ 2 passes through the origin and opens downward, find: 1 the analytic expression of quadratic function 2. The area of triangle formed by intersection A.B and vertex C of X axis

When the parabola y = - x ^ 2 + 2 (k-1) x + 2k-k ^ 2 passes through the origin, the analytic expression of the quadratic function is y = - x ^ 2-2x = (x + 1) ^ 2 + 1, intersecting with X axis a (0,0), B (- 2,0), and vertex C (- 1,1); △ ABC area = 1. K = 2, the analytic expression of the quadratic function is y = - x ^ 2 + 2x = (x-1) ^ 2 + 1, and X ·