Question 402260
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You want to derive a function of the form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \rho(x)\ =\ ax^2\ +\ bx\ +\ c]


That has the elements


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (0,\, 3),\ (1,\, 10),\  (2,\, 19)]


in the solution set.


Since ordered pairs in the solution set of a function are *[tex \LARGE \left(x,\,\rho(x)\right)], for the first point you can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a(0)^2\ +\ b(0)\ +\ c\ =\ 3]


and for the second you can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a(1)^2\ +\ b(1)\ +\ c\ =\ 10]


and for the third:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a(2)^2\ +\ b(2)\ +\ c\ =\ 19]


resulting in a system of three linear equations:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0a\ +\ 0b\ +\ c\ =\ 3]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ =\ 10]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2b\ +\ c\ =\ 19]


Solve the system to get the coefficients for your desired function.


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