Question

Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 2, and 2 Which of the following functions best represents the graph?

f(x) = x3 + x2 − 4x − 4
f(x) = x3 + x2 − x − 1
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 6x − 12

Answer 1

f(x) = x³ + 3x² − 4x − 12

Explanation:

You want the function represented by the graph of a cubic with x-intercepts at -3, -2, and +2.

Polynomial

The factor corresponding to an x-intercept of p is (x -p). The given x-intercepts mean the factored polynomial is ...

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

Expanding that gives ...

f(x) = x³(1·1·1) +x²(3 +2 +(-2)) +x(3·2 +3(-2) +2(-2)) +(3)(2)(-2)

f(x) = x³ +3x² -4x -12