Find the range of f(x) = 2x^2 - x - 1.
How is this done algebraically?
We observe that the given function is a quadratic, whose graph opens upwards since the coefficient on the squared term is positive. So, we know there is no upper bound on the range. Thus the lower bound will occur on the axis of symmetry:
$\displaystyle x=-\frac{-1}{2(2)}=\frac{1}{4}$
$\displaystyle f_{\min}=f\left(\frac{1}{4}\right)=?$