The parabola with (1,2) as vertex intersects with X-axis at a and B, intersects with Y-axis at m, and the coordinate of a is (- 1,0). The area of △ AMB is calculated

The parabola with (1,2) as vertex intersects with X-axis at a and B, intersects with Y-axis at m, and the coordinate of a is (- 1,0). The area of △ AMB is calculated

Let y = a (x-1) 2 + 2, ∵ a coordinate be (- 1,0), ∵ a (- 1-1) 2 + 2 = 0, the solution be a = - 12, ∵ y = - 12 (x-1) 2 + 2 = - 12x2 + X + 32, let y = 0, then - 12x2 + X + 32 = 0, arrange x2-2x-3 = 0, solve X1 = - 1, X2 = 3, ∵ point B coordinate be (3,0), ∵ a (- 1,0), ∵ AB = 3 - (- 1) = 4, let x = 0, then y = 32, ∵ point m coordinate be (0,32), △ am The area of B = 12 × 4 × 32 = 3