Question

已知抛物线Y=ax的平方+b+c开口向下,并且经过A(0,1)和 M(2,-3)两点,如果抛物线与X轴交与B,C两点,且

Answer 1

y=ax^2+bx+c

A:1=c

M:-3=a*4+b*2+c => b=-2-2a

x1*x2=c/a=1/a

设x10,B(x1,0),C(x2,0),坐标原点O

AOB相似于COA

AO:BO=CO:AO

AO^2=BO*CO

1=|x1*x2|=-1/a

a=-1

b=0

y=-x^2+1