This topic is the finale of quadratic function, which comprehensively examines the image and properties of quadratic function, undetermined coefficient method, coordinate characteristics of points on the function image, parallelogram, translation transformation, graphic area calculation and other knowledge points, and it is difficult. You really need to use your head. I have to think about it.

Then, the answer is this/exercise/math /798842. The second question, the key to solving the problem is to get it according to the definition of parallelogram, and then list the equations to solve; The third question, the key to solving the problem is expression, pay attention to the calculation method of graphic area.

As shown in the figure, A (1, 0) and B (3 3,0) are perpendicular to the X axis, and the straight line y=4-x intersects C and D respectively. Parabola y = the square of y=ax +bx+c passes through o, c, d, c and d respectively.

(1) Find the expression of parabola;

(2) Point M is the moving point on the straight line OD, and the vertical line with M as the X axis intersects with the parabola at point N. Ask whether there is such a point M, and the quadrilateral with vertices A, C, M and N is a parallelogram. If it exists, find the abscissa of this point m; If it does not exist, please explain the reason;