Which of the following graphs could be the graph of the function f(x)=-0.08x(x^2-11x+18)?

option C

Step-by-step explanation:

f(x)=-0.08x(x^2-11x+18)

Factor the parenthesis and find out the x intercepts

(x^2-11x+18)

We find out two factors whose product is 18 and sum is -11

-9  and -2 gives us product 18

-9  -2 gives us sum -11

(x^2-11x+18) =(x-9)(x-2)

f(x)=-0.08x(x^2-11x+18)

f(x)= -0.08x(x-9)(x-2)

set f(x) =0  and solve for x

-0.08x(x-9)(x-2) =0

-0.08x =0, so x=0

x-9 = 0 , so x=9

x-2 =0 , so x=2

x intercepts are (0,0) (2,0)  and (9,0)

x intercepts are not repeating

so the graph crosses x -axis at x=0, 2,9

option C is correct

The graph is attached below4