Question

二次函数y=(x+m)^2-2(x+m)-3的图象与x轴交于A、B两点,C为该抛物线顶点,且△ABC的面积为______

Answer 1

y=(x+m)^2-2(x+m)-3=0,(x+m-3)(x+m+1)=0,x=3-m或x=-1-m,A、B两点为(3-m,0),(-1-m)

y=(x+m)^2-2(x+m)-3=x^2+2(m-1)x+m^2-3=(x+(m-1))^2+2m-4,C的坐标为(m-1,2m-4),且判别式=[2(m-1)]^2-4(m^2-3)=-8m+16>=0,m