例1已知二次函数y=ax~2+bx+c(a≠0)的图象经过点(-1,7),且在x轴上截得的线段长度为3,图象的对称轴为直线x=1,求这个二次函数解析式.解因为二次函数图象的对称轴是x=1,在x轴上截得的线段的长度是3,结合图象的对称性可知y=ax~2+bx+c(a≠0)与x轴的 Example 1 It is known that the image of the quadratic function y = ax ~ 2 + bx + c (a ≠ 0) passes through the point (-1,7) and the length of the line segment taken on the x axis is 3, Since the axis is a straight line x = 1, find this quadratic function. Since the symmetry axis of the quadratic function is x = 1 and the length of the line segment taken on the x axis is 3, the symmetry of the image y = ax ~ 2 + bx + c (a ≠ 0) and the x-axis