Question

Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2

Which of the following functions best represents the graph?

f(x) = x3 + x2 − 4x − 4
f(x) = x3 + 4x2 − x − 4
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 4x − 8

Answer 1

Hello,

A cubic polynomial with -2,1,2 as roots is
f(x)=k*(x+2)(x+1)*(x-2)=k(x²-4)(x+1)=k(x^3+x²-4x-4)

Looking the answers ==>k=1


==>Answer A

Answer 2

`f(x)=x^3+x^2-4x-4`

Explanation:

Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2

x intercepts are -2, -1, 2

We write the x intercepts in factor form

f(x)= (x-p)(x-q)(x-r)

where p, q and r are the x intercepts

f(x)= (x-(-2))(x-(-1))(x-2)

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

now we multiply the parenthesis using FOIL method

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

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

now we multiply with (x-2)

x^3-2x^2 +3x^2-6x+2x-4

combine like terms

`f(x)=x^3+x^2-4x-4`