Question 986496
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The sign on the lead coefficient tells you which way the parabola opens.  Positive (like your example) opens up, meaning that the value at the vertex is a minimum.  Negative, it opens down, so the value at the vertex is a maximum.


The value of *[tex \Large x] that locates the vertex is given by the opposite of the coefficient on the first degree term divided by twice the lead coefficient.  For your problem, *[tex \Large x_v\ =\ \frac{-2}{2(1)}\ =\ -1].


The minimum (or maximum) value is simply the *[tex \Large x_v] value substituted into the function everywhere you see an *[tex \Large x].  You have to do the arithmetic.


For a parabola that opens upward, the range is the minimum value to positive infinity.  For a parabola that opens downward, the range is minus infinity to the maximum value.


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

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \