Question

Plot the x- and y- intercepts of the function.
f(x)=x3+2x2-x-2

Answer 1

see below for a plot

Explanation:

The y-intercept is where x=0:

f(0) = 0^3 +2·0^2 -0 -2 = -2

The x-intercepts can be found where f(x)=0:

0 = x^3 +2x^2 -x -2 = x^2(x +2) -1(x +2) = (x^2 -1)(x +2)

0 = (x +1)(x -1)(x +2)

The values of x that make these factors zero are {-2, -1, 1}.

The x-intercepts are (-2, 0), (-1, 0), (1, 0). The y-intercept is (0, -2).