Observe the graph:

Since the graph has three turning points, the degree of the function is at least .

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The curve crosses the -axis at and .

So the polynomial function has a real zeros at and . 

Note that because is a minimum point it occurs twice as a zero of the function.

If  is a real zero of a polynomial function , then is a factor of .

Therefore, and are factors of .

So far, we have the function is .

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The -intercept of the graph is .

This means .

Substitute in .

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Therefore, possible polynomial function is .

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