Question

Построить график функции y=x*|x-1|+|x+2|

Answer 1

$x-1=0, \ x=1, \\ x+2=0, \ x=-2, \\ 1) \ x\ \textless \ -2, \ x-1\ \textless \ 0, \ x+2\ \textless \ 0, \\ y=x(1-x)-(x+2)=x-x^2-x-2=-x^2-2, \\ 2) \ -2\leqx\ \textless \ 1, \ x-1\ \textless \ 0, \ x+2\geq0, \\ y=x(1-x)+(x+2)=x-x^2+x+2=-x^2+2x+2=\\=-(x^2-2x+1)+3=-(x^2-1)+3, \\ 3) \ x\geq1, \ x-1\geq0, \ x+2\ \textgreater \ 0, \\ y=x(x-1)+(x+2)=x^2-x+x+2=x^2+2$