Question 799088
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First thing you must learn:  X is NOT the same thing as x.  The only way we have to communicate is in writing, so make SURE you don't type something incorrectly.


Second, ^ (Shift-6) means "raise to the power", so x^2 means *[tex \Large x^2]


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


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


The *[tex \Large y]-coordinate of the vertex is *[tex \Large y_v\ =\ f(x_v)\ =\ a\left(-\frac{b}{2a}\right)^2\ +\ b\left(-\frac{b}{2a}\right)\ +\ c]


The *[tex \Large x]-intercepts, if they exist, are at *[tex \Large (x_1,0)] and *[tex \Large (x_2,0)] where


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ =\ \frac{-b\ +\ \sqrt{b^2\ -\ 4ac}}{2a}]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_2\ =\ \frac{-b\ -\ \sqrt{b^2\ -\ 4ac}}{2a}]


The equation of the axis of symmetry is *[tex \Large x\ =\ x_v], which is to say the vertical line through the vertex.


It looks exactly like a parabola.


It opens upward if *[tex \Large a\ >\ 0], downward otherwise.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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