25. The parabola y = - x2 moves upward by 4 units, and then moves to the right by M (M > 0) units, just passing through the origin. The parabola after translation intersects with the straight line y = 2x The parabola y = - x2 moves upward by 4 units, then moves to the right by M (M > 0) units, and then just passes through the origin. The translated parabola and the straight line y = 2x intersect at two points a and B (a is on the left side of B) (1) The analytical formula of parabola after translation (2) Finding the coordinates of two points a and B (3) Point P is a moving point on the parabola above the straight line y = 2x. Whether there is a maximum area of △ ABP, if there is a result, then the coordinates of point P can be obtained. If there is no reason, the area of △ ABP can be calculated, (4) Point q is a point in the coordinate plane. If △ ABQ is an isosceles right triangle and ∠ BAQ = 90 °, write directly the coordinates of the point Q satisfying the condition, and answer directly whether any of these points are on the parabola after translation?

25. The parabola y = - x2 moves upward by 4 units, and then moves to the right by M (M > 0) units, just passing through the origin. The parabola after translation intersects with the straight line y = 2x The parabola y = - x2 moves upward by 4 units, then moves to the right by M (M > 0) units, and then just passes through the origin. The translated parabola and the straight line y = 2x intersect at two points a and B (a is on the left side of B) (1) The analytical formula of parabola after translation (2) Finding the coordinates of two points a and B (3) Point P is a moving point on the parabola above the straight line y = 2x. Whether there is a maximum area of △ ABP, if there is a result, then the coordinates of point P can be obtained. If there is no reason, the area of △ ABP can be calculated, (4) Point q is a point in the coordinate plane. If △ ABQ is an isosceles right triangle and ∠ BAQ = 90 °, write directly the coordinates of the point Q satisfying the condition, and answer directly whether any of these points are on the parabola after translation?

(1) Y = - (x-m) 2 + 4 and M > 0, substituting (0,0), the solution is m = 2Y = - (X-2) 2 + 4 = - x2 + 4x (2) y = - x2 + 4x and y = 2x simultaneously - (X-2) 2 + 4 = 2x, the deformation is: X2 - 2x = 0, the solution is x = 0 or x = 2 coordinates: a (0,0) B (2,4) (3) have