Question

Plot the x- and y- intercepts of the function.

Answer 1

y intercept = -2

x intercepts = -2,-1,1

Explanation:

f(x) = x^3 + 2x^2 -x-2

Set this equation equal to zero to find the x intercepts.

Factoring by grouping

0 =x^3 -x +2x^2 -2

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

Factoring out the (x^2-1)

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

Factoring the first term using the difference of squares (a^2-b^2) = (a-b)(a+b)

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

Using the zero product property

x-1 = 0 x+1 = 0 x+2 =0

x=1, x=-1 x=-2

The x intercepts are -2, -1, 1

To find the y intercepts, set x=0

y = x^3 + 2x^2 -x-2

y = 0 -2

y = -2