Pre-Calculus, 9th edition
65

 PAGE: 185 SET: Exercises PROBLEM: 65

Observe the graph :

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

The third degree polynomial should be in the form .

The curve crosses the - axis at and .

So the polynomial function has a real zeros at and

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

Therefore, and are factors of .

Thus, the polynomial function is .

.

The -intercept of the graph is .

This means .

Substitute in .

Therefore, possible polynomial function is .

.

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