Respuesta :

frika

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

[tex]f(x)=(x-(-2))(x-0)(x-3)=x(x+2)(x-3).[/tex]

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).

alinakincsem

Answer:

The last graph at bottom right.

Step-by-step 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:

[tex]f(x) = (x - (-2)) (x - 0) (x - 3)[/tex]

[tex]f (x) = (x + 2) (x) (x - 3) = x (x + 2) (x - 3)[/tex]

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).

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