As shown in the figure, the parabola y = ax ^ 2 + 3 / 2x + C passes through the origin O and a (4,2), intersects the x-axis with point C, and the point m.n starts from the origin 0 at the same time, and the point m takes two single points The velocity of bit / s moves along the positive direction of y-axis, and point n moves along the positive direction of x-axis at the velocity of 1 unit / s. when one of the points stops moving, the other point stops (1). Find the analytical formula of parabola and the coordinates of point C; (2) in the process of point M. n moving, if the line Mn and OA intersect at point G, it is to judge the position relationship between Mn and OA, and explain the reason; Is there any time t that makes a quadrilateral with O, P, a and C as fixed points an isosceles trapezoid? If so, please explain the reason. {please hurry up,

As shown in the figure, the parabola y = ax ^ 2 + 3 / 2x + C passes through the origin O and a (4,2), intersects the x-axis with point C, and the point m.n starts from the origin 0 at the same time, and the point m takes two single points The velocity of bit / s moves along the positive direction of y-axis, and point n moves along the positive direction of x-axis at the velocity of 1 unit / s. when one of the points stops moving, the other point stops (1). Find the analytical formula of parabola and the coordinates of point C; (2) in the process of point M. n moving, if the line Mn and OA intersect at point G, it is to judge the position relationship between Mn and OA, and explain the reason; Is there any time t that makes a quadrilateral with O, P, a and C as fixed points an isosceles trapezoid? If so, please explain the reason. {please hurry up,

(1) According to the meaning of the title, the coordinates of point a are (4,2), and the coordinates of point o are (0,0). Substituting them into the analytical formula, we get C = 016a + 3 / 2 × 4 + C = 2, and the solution is: C = 0A = - 14 ⊥ the analytical formula of parabola is y = - 14x2 + 3 / 2x; if y = 0, then 0 = - 14x2 + 3 / 2x, and the solution is X1 = 0, X2 = 6, so the point C coordinate is (6,0); (2) ① Mn ⊥ OA