Observe the graph :

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

The fourth degree polynomial function be in the form .

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 .

Thus, the polynomial function is .

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The -intercept of the graph is .

This means .

Substitute in .

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Therefore, the possible polynomial function is .

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