Question 320764
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Put your function into standard, namely *[tex \LARGE f(x)\ =\ ax^2\ +\ bx\ +\ c], form.


The *[tex \LARGE x]-coordinate of the vertex is given by *[tex \LARGE x_v\ =\ \frac{-b}{2a}]


The *[tex \LARGE y]-coordinate of the vertex is the value of the function at the *[tex \LARGE x]-coordinate of the vertex, to wit:


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


The line of symmetry is the equation *[tex \LARGE x\ =\ x_v]


The maximum or minimum value of the function is *[tex \LARGE y_v\ =\ f(x_v)].  It is a minimum if the lead coefficient (the *[tex \LARGE a] in  *[tex \LARGE ax^2\ +\ bx\ +\ c]) is positive and a maximum if it is negative.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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