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Who can tell me the original question of the last math problem in the 20 12 Sichuan Guangyuan senior high school entrance examination?
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24. As shown in the figure, the parabola y = AX2+2ax+c (a ≠ 0) intersects with the Y axis at point C (0,4) and with the X axis at point A (-4,0) and point B (1), so as to find the analytical formula of the parabola;

(2) Point Q is the moving point on the AB line, and the intersection point Q is QE∑AC.

Cross BC at point E and connect CQ. △ When the area of △CEQ is the largest.

When, find the coordinates of Q point;

(3) The moving straight line L parallel to the X axis intersects the parabola at point P, and

The straight line AC intersects with point F, and the coordinate of point D is (-2,0). Ask.

Is there a straight line l that makes △ODF an isosceles triangle? If it exists,

Find the coordinates of point f; If it does not exist, please explain why.