Question

Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 1, and 3 Which of the following functions best represents the graph?

a f(x) = x3 + x2 − 9x − 9
b f(x) = x3 + 4x2 − x − 4
c f(x) = x3 + 3x2 − 3x − 9
d f(x) = x3 + 2x2 − 4x − 8

Answer 1

The correct answer is Choice A.

If you graph the function on a graphing calculator, you will find that it matches all of the necessary parts. If falls to the left and rises to the right.

It also has zeros at -3, -1 and 3.

Answer 2

Option A is correct .i.e, f(x) = x³ + x² - 9x - 9 represent the graph best.

Explanation:

Given: x-intercepts of cubic polynomial are -3 , -1 and 2

To find the cubic polynomial, f(x)

We know the x-intercept of cubic polynomial are the zeroes of the polynomials.

So the factors of cubic polynomials we get from zeroes are ( x + 3 ) , ( x + 1 ) and ( x - 3 )

Cubic polynomial , f(x) = ( x + 3 ) ( x + 1 ) ( x - 3 )

= ( x + 3 ) ( x - 3 ) ( x + 1 )

(using identity: (a-b) (a+b) = a² - b²)

= ( x² - 9 ) ( x + 1 )

= x² ( x + 1 ) - 9 ( x + 1 )

= x³ + x² - 9x - 9

Therefore, Option A is correct .i.e, f(x) = x³ + x² - 9x - 9 represent the graph best.