Question 633244
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Consider the function *[tex \LARGE f(x)\ =\ ax^2\ +\ bx\ + c]


If *[tex \LARGE (5,-1)] is a point on the function, then the coordinates of the point must satisfy the function, hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a(5)^2\ +\ b(5)\ +\ c\ =\ -1]


Also, since *[tex \LARGE (5,-1)] is the vertex and *[tex \LARGE (8,17)] is a point on the graph, symmetry says that *[tex \LARGE (2,17)] is also a point on the graph.  That leads us to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a(8)^2\ +\ b(8)\ +\ c\ =\ 17]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a(2)^2\ +\ b(2)\ +\ c\ =\ 17]


Therefore, solve the 3X3 system:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \,4a\ +\ 2b\ +\ c\ =\ 17]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 25a\ +\ 5b\ +\ c =\ -1]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 64a\ +\ 8a\ +\ c\ =\ 17]




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