Question 661813
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There are a couple of ways to go about this.  The easy way is to plug your points into a graphing calculator or a graphing program on your computer and let the computer figure it out.


The hard way is as follows.


Five points uniquely determine a 4th degree polynomial equation.  The general form of a 4th degree polynomial function is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ y\ =\ ax^4\ +\ bx^3\ +\ cx^2\ +\ dx\ +\ e]


Start with your first point and substitute the values:


*[tex \LARGE \ \ \ \ \ \ \ \ \ 89\ =\ a(-4)^4\ +\ b(-4)^3\ +\ c(-4)^2\ +\ d(-4)\ +\ e]


Simplify:


*[tex \LARGE \ \ \ \ \ \ \ \ \ 256a\ -\ 64b\ +\ 16c\ -\ 4d\ +\ e\ =\ 89]


Similarly, using the other points produce:


*[tex \LARGE \ \ \ \ \ \ \ \ \ 81a\ -\ 27b\ +\ 9c\ -\ 3d\ +\ e\ =\ 7]


*[tex \LARGE \ \ \ \ \ \ \ \ \ a\ -\ b\ +\ c\ -\ d\ +\ e\ =\ -1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ +\ d\ +\ e\ =\ -1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ 256a\ +\ 64b\ +\ 16c\ +\ 4d\ +\ e\ =\ 329]


Then use whatever method you like to solve the 5X5 system of equations to determine your coefficients for the polynomial function.  Hint:  Multiply the third equation by -1, then add the third and 4th equations.  The whole thing will reduce to *[tex \LARGE -b\ =\ d].  Go back and substitute *[tex \LARGE -b] for *[tex \LARGE d] in the first 4 equations giving yourself a much simpler 4X4 system to solve.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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