Answer:
The correct answer option is C. [tex]f(x)=-2x^3-2x^2+12x[/tex].
Step-by-step explanation:
From the given graph of the polynomial function, we can see that the graph passes through the following points: [tex](-3,0), (0,0)[/tex] and [tex](2,0)[/tex].
So the roots or zeros of this polynomial function are: [tex]-3,0[/tex] and [tex]2[/tex].
Now, we'd graph the equation of the given polynomial and will check for roots and end behavior of the graph.
Therefore, the polynomial function that is represented by the graph is:
[tex]f(x)=-2x^3-2x^2+12x[/tex]
