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Example Question #2 : Functions And Graphs
What is the minimal value of
over all real numbers?
No minimum value.
Since this is an upwards-opening parabola, its minimum value will occur at the vertex. The -coordinate for the vertex of any parabola of the form
We plug this value back into the equation of the parabola, to find the value of the function at this .
Thus the minimal value of the expression is .