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

Answer 1

Answer:

f(x) = x3 + 3x2 − 4x − 12

Step-by-step explanation:

A polynomial which falls tot he left and rises to the right is a function with a positive leading coefficient. Its formed by the x-intercepts or zeros x = -3, -2 and 2. The zeros form the factors (x+3)(x+2)(x-2). Multiply the factors using the distributive property to find the function in standard form.

(x+3)(x+2)(x-2)

(x^2 + 3x + 2x + 6)(x-2)

(x^2 + 5x + 6)(x-2)

x^3 + 5x^2 + 6x -2x^2 - 10x - 12

x^3 + 3x^2 - 4x - 12