SOLUTION: determine the poynomial whose graph passes through the points (-1,1), (0,-2), (1,0), and (2,-1)

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Question 262271: determine the poynomial whose graph passes through the points (-1,1), (0,-2), (1,0), and (2,-1)
Answer by solver91311(24713) About Me  (Show Source):
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Plotting the given points looks like it might be a cubic, so let's presume a 3rd degree polynomial and see what happens.



So if the point (-1,1) is on the graph, then:



And if the point (0,-2) is on the graph, then:



And if the point (1,0) is on the graph, then:



And if the point (2,-1) is on the graph, then:



Note that the second equation reduces to



Using that information and simplifying we get:









The solution to the above system is:



Verification of the solution of the linear system is left as an exercise for the student.

Hence the desired polynomial is:




John