Question 486178
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An equation for a parabola can take the form:


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


Any ordered pair *[tex \Large \left(x,\rho(x)\right)]


will satisfy the equation, so given that *[tex \Large (-3,7)] is a point on the parabola:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a(-3)^2\ +\ b(-3)\ +\ c\ =\ 7]


Which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9a\ -\ 3b\ +\ c\ =\ 7]


Likewise you can derive:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2b\ +\ c\ =\ 9]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 36a\ +\ 6b\ +\ c\ =\ -2]


Solve the system of equations to obtain the coefficients of your parabolic function.


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