Question

The degree of the polynomial function f(x) is 3

The roots of the equation f(x) = 0 are -2, 0, and 3

Which graph could be the graph of f(X)?

Answer 1

The last graph at bottom right.

Explanation:

We are given the degree of the polynomial function f(x) to be 3; and

the roots of the equation f(x) to be 0 and -2, 0, and 3.

So we will put these values in the polynomial function of degree 3 to get:

`f(x) = (x - (-2)) (x - 0) (x - 3)`

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

According to this, the x - intercepts of this function on the graph will be:

(0, 0)

(-2, 0)

(3, 0)

So we will look for a graph which intercepts the x-axis at these points.

Therefore, the last graph at the bottom right satisfies the conditions and is the graph of f(x).

Answer 2

If the roots of the equation f(x) = 0 are -2, 0, and 3 and the degree of the polynomial function f(x) is 3, then the polynomial has a form

`f(x)=(x-(-2))(x-0)(x-3)=x(x+2)(x-3).`

The x-intercepts of the graph of this polynomial function are:

• (-2,0);
• (0,0);
• (3,0).

These points are x-intercepts of the graph of the last function (option D).