化简y=(根号4x²+4x+1)+(根号4x²-12x+9)还要画出简图,

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/09 05:35:24
化简y=(根号4x²+4x+1)+(根号4x²-12x+9)还要画出简图,

化简y=(根号4x²+4x+1)+(根号4x²-12x+9)还要画出简图,
化简y=(根号4x²+4x+1)+(根号4x²-12x+9)
还要画出简图,

化简y=(根号4x²+4x+1)+(根号4x²-12x+9)还要画出简图,
y=√(4x^2+4x+1)+√(4x^2-12x+9)
=√(2x+1)^2+√(2x-3)^2
=|2x+1|+|2x-3|
1)
2x+1≥0
2x-3≥0
即x≥3/2时
原式=2x+1+2x-3=4x-2
2)
2x+1≤0
2x-3≤0
即x≤-1/2时
原式=-2x-1-2x+3=-4x+2
3)
-1/2<x<3/2时
原式=2x+1-2x+3=4

分别讨论2x+1和2x-3与0的大小关系
所以x<=-1/2时y=-2x-1-2x+3=2-4x
-1/2<=x<=3/2时y=2x+1+3-2x=4
x>=3/2时y=2x+1+2x-3=4x-2

y=(根号4x²+4x+1)+(根号4x²-12x+9)
y=2x+1+2x-3
y=4x-2

=(2x+1)+(2x-3)=4x-2

当x≤-1/2时
=-2x-1-2x+3=-4x+2
当-1/2<x<2/3时
=2x+1-2x+3=4
当x≥2/3
=(2x+1)+(2x-3)=4x-2