已知三个点的座标,如何求二次函数的系数?已知（x1,y1),(x2,y2),(x3,y3)求y=a+bx+cx^2中的a、b和c的公式

Question

已知三个点的座标,如何求二次函数的系数?
已知（x1,y1),(x2,y2),(x3,y3) 求y=a+bx+cx^2中的a、b和c的公式

Answer 1

y1=a+bx1+cx1^2 y2=a+bx2+cx2^2 y3=a+bx3+cx3^2 (y1-y2)/(x1-x2)=b+c(x1^2-x2^2)/(x1-x2) (y2-y3)/(x2-x3)=b+c(x2^2-x3^2)/(x2-x3) (y1-y2)/(x1-x2)-(y2-y3)/(x2-x3)=c((x1^2-x2^2)/(x1-x2)-(x2^2-x3^2)/(x2-x3)) c=[(y1-y2)/(x1-x2)-(y2-y3)/(x2-x3)]/((x1^2-x2^2)/(x1-x2)-(x2^2-x3^2)/(x2-x3)) b=-c(x2^2-x3^2)/(x2-x3)+(y2-y3)/(x2-x3) a=y1-bx1-cx1^2