Substituting the coordinates of two points into the analytical formula, we can solve b=3/4 (not equal to 0), so we can determine that B is wrong (the primary term system is not 0, so the symmetry axis cannot be Y axis); And because of a>0, b>0, the value of -b/2a is negative, so c is also wrong (the symmetry axis should be on the left side of the Y axis); Finally, analyzing A and D, the symmetry axis x=-b/2a, where when a=3/2, the symmetry axis is x= 1, and when A takes any other number greater than 0 and not equal to 3/2, the symmetry axis is not x= 1, so A is also wrong, and the correct option is D.