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Solution: In the function y=-3x+3, let x=0, then y=3, that is, the intersection of the straight line y=-3x+3 and the Y axis is (0,3).

Let y=0, then -3x+3=0, x= 1, that is, the intersection of the straight line y=-3x+3 and the x axis is (1, 0).

Because the quadratic function y=ax? The image of +bx+c passes through the intersection of the straight line y=-3x+3 with the X axis, Y axis and point (-3,0).

That is, through the point (0,3) (1,0) (-3,0).

So 3=c

0=a+b+c

0=9a-3b+c

The solution is a=- 1? ，b=-2？ ，c=3

So the analytical formula of this quadratic function is: y=-x? -2x+3