Question 518451
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This is a polynomial function so it is defined for all real numbers.  The graph is a concave up parabola, so the value of the function at the vertex is the minimum value in the range.


For a quadratic function of the form:


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


the coordinates of the vertex are found by:


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


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


Then the range is the interval 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \rho(x_v)\ \leq\ y\ \leq\ \infty]


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