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simmonsl7790
03.10.2019 •
Mathematics
Determine a polynomial function whose graph passes through the given points. 5: (0,-5); (1,-4) ; (-1,-9); (2,-3),
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Ответ:
The interpolating polynomial is
Step-by-step explanation:
First, notice that we want to calculate the interpolating polynomial through the points (0,-5); (1,-4) ; (-1,-9); (2,-3). This means that we want to find a polynomial
such that
We will have four equations, so our polynomial will be, at most, of degree 3. Let us write
The coordinates give us the following equations:
Notice that from the second equation we know that
. Then, we obtained the linear system of equations
which is equivalent to
So, we have reduced our interpolation problem to solve a linear system of equations. Now, notice that if we add the first two equations of the system we obtain
Then, our system becomes
which is equivalent to
Recall that now the first two equations are just the same, so we will use the first and third ones:
If we multiply the first one and add it to the second we get:
Thus, substituting this value in the first equation:
Summing up all our results we get that the interpolating polynomial is
Ответ: