SOLUTION: What polynomial has a graph that passes through the given points (-2, 2) (-1, -1) (1, 5) (3, 67)
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Question 623652: What polynomial has a graph that passes through the given points (-2, 2) (-1, -1) (1, 5) (3, 67)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Since you have 4 points, you need a 4-term, which is to say a 3rd degree, polynomial of the form:
\ =\ ax^3\ +\ bx^2\ +\ cx\ +\ d)
Using the data in your first point:
\ =\ a(-2)^3\ +\ b(-2)^2\ +\ c(-2)\ +\ d\ =\ 2)
which yields a four variable linear equation:
Using similar logic, write three more 4 variable linear equations using the data in the other three points yielding, in toto, a 4X4 system of equations.
Solve the 4X4 system by any convenient (relatively speaking that is) means. I used the MDETERM function in Excel and then apply Cramer's Rule. The ordered quadruple element of the solution set to the 4X4 (it is an independent and consistent system, by the way) consists of the 4 coefficients of your desired polynomial.
John
My calculator said it, I believe it, that settles it
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