Question

Use finite differences to determine the degree of the polynomial function that fi ts the data. Then use technology to find the polynomial function.

(-6, 744), (-4, 154), (-2, 4), (0, -6), (2, 16), (4, 154), (6, 684), (8, 2074), (10, 4984)
The degree of the polynomial function is
f(x) =

Answer 1

To determine the degree of the polynomial function that fits the data, use finite differences. The degree of the polynomial function is 3.

Step-by-step explanation:

To determine the degree of the polynomial function that fits the data, we can use finite differences. Finite differences involve finding the differences between consecutive terms in the y-values. If the differences remain constant, it suggests a polynomial function.

Let's calculate the first differences for the given data:

{-590, -150, -10, 22, 138, 530, 384, 510, 1910}

The first differences are not constant, which means the function is not linear. We can then calculate the second differences:

{440, 140, 32, 116, 392, -146, 126, 1400}

The second differences are also not constant, indicating that the function is not quadratic. We continue this process until we find a constant difference, which will indicate the degree of the polynomial function. In this case, after calculating the third differences, we get:

{-300, -108, 84, 276, -538, 272, 1274}

The third differences are constant, and since we needed three sets of differences to achieve this, the degree of the polynomial function is 3.