若已知抛物线上三点坐标为(1,0);(-1,-4);(0,-3)求其表达式

问题描述:

若已知抛物线上三点坐标为(1,0);(-1,-4);(0,-3)求其表达式

设y=ax2+bx-3,
由题意得:a+b-3=0,a-b-3=-4.
解得: a=1,b=2
所以y=x2+2x-3

设表达式为:y=ax^2+bx+c 则有:a+b+c=0 `````````````````````1a-b+c=-4``````````````````````2c=-3```````````````````````````3联立1、2、3解得:a=1,b=2,c=-3所以可得:y=x^2+2x-3