Answer:
1) (0,-2)
2) [tex](-2,0),(-1,0),(1,0)[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=x^3+2x^2-x-2[/tex]
At y-intercept [tex]x=0[/tex]
This implies that;
[tex]f(0)=(0)^3+2(0)^2-0-2[/tex]
[tex]f(0)=-2[/tex]
The y-intercept is
(0,-2).
At x-intercept [tex]f(x)=0[/tex]
[tex]x^3+2x^2-x-2=0[/tex]
Factor to obtain;
[tex](x+1)(x-1)(x+2)=0[/tex]
This implies that;
[tex]x=-2,x=-1,x=1[/tex]
The x-intercepts are
[tex](-2,0),(-1,0),(1,0)[/tex]
The points are plotted in the file attached.
