From A Graph

The steps to model a polynomial function from a graph are very similar to the steps used when given a table. First, determine the zeros of the function by looking at the graph. Second, turn each zero into a factor of the function. Finally, determine the factored form of the polynomial.**Example 1** Determine the function that models the graph below:

*Step 1.* Determine the zeros of the function.

(-1, 0), (0, 0), (5, 0)

*Step 2.* Turn each zero into a factor of the function.

Since *x* = -1, then (*x* + 1) is a factor of the polynomial.

Since *x* = 0, then (*x*) is a factor of the polynomial.

Since *x* = 5, then ( *x* - 5) is a factor of the polynomial.