Question 443774
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Given a quadratic function


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


an equation of the axis of symmetry is *[tex \Large x\ =\ \frac{-b}{2a}]


The maximum or minimum of a quadratic function is the value of the funcition at the *[tex \Large x]-coordinate of the vertex.  The *[tex \Large x]-coordinate of the vertex is found by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_v\ =\ \frac{-b}{2a}]


And then the value of the funcition at the vertex is the function evaluated at *[tex \Large x_v]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y_v\ =\ \rho(x_v)\ =\ \rho\left(\frac{-b}{2a}\right)\ =\ a\left(\frac{-b}{2a}\right)^2\ +\ b\left(\frac{-b}{2a}\right)\ +\ c]


If the lead coefficient, *[tex \Large a], is positive, then the graph opens upward and the value of the function at the vertex is a minimum.  If the lead coefficient is negative, then the graph opens downward and the value of the function at the vertex is a maximum.


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