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对于二次函数y=ax~2+bx+c(a≠0),当函数值y=0时,可以得到一元二次方程ax~2+bx+c=0.这说明二次函数与一元二次方程有着必然的联系.从图象上看,二次函数y=ax~2+bx+c的图象与x轴交点的横坐标就是一元二次方程ax~2+bx+c=0的根.二次函数的图象与x轴的位置关系有三种:①有一个公共点;②有两个公共点;③没有公共点.这对应着一元二次方程ax~2+bx+c=0根的三种情形:①有两个相等的实数根;②有两个不相等的实数根;③没有实数
For the quadratic function y = ax ~ 2 + bx + c (a ≠ 0), the quadratic equation ax ~ 2 + bx + c = 0 can be obtained when y = 0. This shows that the quadratic function is equivalent to one yuan Quadratic equation has a necessary relationship.From the image point of view, quadratic function y = ax ~ 2 + bx + c image x-axis intersection point of the abscissa is the quadratic equation ax ~ 2 + bx + c = 0 The quadratic function of the image and the x-axis position relationship in three ways: ① There is a common point; ② There are two common points; ③ There is no common point. This corresponds to a quadratic equation ax ~ 2 + bx + c = 0 root three cases: ① There are two equal real roots; ② There are two real roots that are not equal; ③ There is no real number