When c= 1/3 and discriminant = 0, it is known from Vieta's theorem that the equation has only one root, which means that the parabola has only one intersection with the X axis. Check again, the point is exactly-1

But when c< 1/3, discriminant >; 0, indicating that the parabola has two intersections with the X axis. However, there is only one common point in the title requirements (-1, 1), and it must be ensured that when x =- 1 and x = 1, the sign of y value is opposite, so as to ensure that there is only one common point in the subinterval.

The nature of these two situations is different. In the former case, there is only one intersection point, and in the latter case, when there are two intersections between the parabola and the X axis, there is only one intersection point in the interval of (-1, 1).

2) The third question.

Firstly, x 1=0, y >；; 0 and x2= 1, y>0, and judge the sizes of a and c and a >; C>0, so we can judge the opening direction of parabola.

Then through the discriminant and the ac relation obtained above, it is judged that there are two intersections between the parabola and the X axis, because the opening is upward and the vertex must be below the X axis.

Then through the relationship of abc, it is judged that the symmetry axis X=-b/3a is between x= 1/3 and x=2/3.

When x = 0 and x = 1 are passed, y is greater than 0, and there are two things in common between the judgments (0, 1).