Given the set points k+1: (-1,,0) and (2,5), find the quadratic polynomial interpolate

The interpolating polynomial is .

Step-by-step explanation:

We want to find a quadratic polynomial such that , and . In order to do this let us write .

Now, evaluating the polynomial in the points -1, 1 and 2 we get

This relations give us a linear system of equations:

where the , and are the unknowns.

The augmented matrix of the system is

In this matrix it is easy to eliminate the 1's of the first column and get

From this matrix we can find the values of each unknown. Notice that the second row gives us that yields .

Then, the third row means that gives . So, .

Finally, the first row is and substituting is that yields .

Therefore, the interpolating polynomial is

.

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