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The ninth grade math book exercises 26. 1 Solve the analytical formula of the function according to the coordinates of three points on the quadratic function image.
General formula of quadratic function y = a 2+bx+c

1, using symmetry, the first two points show that the symmetry axis is the y axis, so y = ax 2+c, and the last two points are substituted, and a= 1.c=2.

2. Using symmetry, the symmetry axis is x= 1, and the analytical formula is Y = A (X- 1) 2+H, and the analytical formula is obtained by substituting the point.

3. Mark these three points first and find that you can't find the symmetry axis like the previous two questions. In order to satisfy the three points on the quadratic function image, we guess that the analytical formula contains absolute values. If there is no absolute value, the image opens up and passes (-2,20) (3,0). Because there is an absolute value, the lower half of the X axis is folded upward and passes through (1, 2).

Therefore, when there is no absolute value, the function passes through (-2,20), (1,-2) and (3,0), and the unknown coefficient is obtained by setting y = a 2+bx+c in the conventional method, and the absolute value needs to be added to this analytical formula.