It is known that the image of parabola y = the square of minus two-thirds x + four-thirds x + 2 intersects with X-axis at two points a and B, intersects with Y-axis at point C, the symmetry axis of parabola intersects with X-axis at point D, and point m starts from point O and moves to point B at a speed of 1 unit length per second. Point m is perpendicular to x-axis and intersects object line at point P (1) Find the coordinates of point B and point C; (2) Suppose that the area of the quadrilateral OmpC is s when the point m moves x (seconds), find the functional relationship between S and X, and point out the value range of the independent variable x

It is known that the image of parabola y = the square of minus two-thirds x + four-thirds x + 2 intersects with X-axis at two points a and B, intersects with Y-axis at point C, the symmetry axis of parabola intersects with X-axis at point D, and point m starts from point O and moves to point B at a speed of 1 unit length per second. Point m is perpendicular to x-axis and intersects object line at point P (1) Find the coordinates of point B and point C; (2) Suppose that the area of the quadrilateral OmpC is s when the point m moves x (seconds), find the functional relationship between S and X, and point out the value range of the independent variable x

1) Sorting: y = (- 2 / 3) x & # 178; + (4 / 3) x + 2 = (- 2 / 3) (X & # 178; - 2x-3) = (- 2 / 3) (x-3) (x + 1)
So X-axis intersection coordinates are (- 1,0), (3,0)
From the following, B (3,0)
When x = 0, y = 2, C (0,2) is obtained
 
2) The quadrilateral OmpC is trapezoidal,
Let m move for x seconds, then the abscissa of M (x, 0), P is x, and the ordinate is (- 2 / 3) x & # 178; + (4 / 3) x + 2
So quadrilateral OmpC area
S=（1/2）*(OC+PM)*OM
=(1/2)[2+(-2/3)x²+(4/3)x+2)]*x
=(-1/3)x^3+(2/3)x^2+2X
(0<x<3)