一元二次方程ax~2+bx+c=0和二次函数y=ax~2+bx+c的关系密不可分。在y=ax~2+bx+c中,当y=0时,就变成了ax~2+bx+c=0。而一元二次方程ax~2+bx+c=0的两根x_1,x_2,就是二次函数y=ax~2+bx+c的图象与x轴交点的横坐标。因此,根与系数的关系不但可以用于方程这中,也常用于二次函数之中。 一 求待定系数的值 例1 抛物线y=x~2-(2m-1)x-2m与x轴的 The relationship between the quadratic equation ax~2+bx+c=0 and the quadratic function y=ax~2+bx+c is inseparable. In y=ax~2+bx+c, when y=0, it becomes ax~2+bx+c=0. The two x_1,x_2 of the quadratic equation ax~2+bx+c=0 are the abscissa of the intersection of the image of the quadratic function y=ax~2+bx+c and the x-axis. Therefore, the relationship between root and coefficient can be used not only in equations but also in quadratic functions. Determine the value of the undetermined coefficient. Example 1 Parabolic y=x~2-(2m-1)x-2m and x-axis