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In the graph below, the coordinates of the indicated point are $(-2,18)$. Construct a polynomial function that might have the given graph. (Use the smallest degree possible.)
Which of the following is a polynomial function that might have the given graph?
A. $f(x)=-\frac{1}{2}(x+1)(x-1)^{2}(x-2)$
B. $f(x)=\frac{1}{2}(x+1)(x-1)^{2}(x-2)$
C. $f(x)=\frac{1}{2}(x+1)(x-1)(x-2)$
D. $f(x)=\frac{1}{2}(x+1)(x-1)(x-2)^{2}$
E. $f(x)=-\frac{1}{2}(x+1)(x-1)(x-2)^{2}$
F. $f(x)=\frac{1}{2}(x+1)^{2}(x-1)(x-2)$

Step 1 ：The problem is asking for a polynomial function that might have the given graph. The graph is not provided here, but we know that the point (-2,18) lies on the graph. We can use this information to test each of the given polynomial functions. If the function evaluates to 18 when x is -2, then it could be the function for the graph.

Step 2 ：Test each function by substituting x=-2 into each function.

Step 3 ：The function that evaluates to 18 when x is -2 is B. Therefore, the polynomial function that might have the given graph is B.

Step 4 ：Final Answer: \(\boxed{B. f(x)=\frac{1}{2}(x+1)(x-1)^{2}(x-2)}\)