# How do you find the domain and range of y = x^2 - x + 5?

Domain is all real numbers and the range is all real numbers $\ge$ $\frac{19}{4}$.
The easiest way is to rewrite it as y= ${\left(x - \frac{1}{2}\right)}^{2}$ +$\frac{19}{4}$. This represents a parabola opening up with its vertex at ( $\frac{1}{2}$, $\frac{19}{4}$). This clearly depicts the domain as all real numbers (-inf, inf) and range as all real numbers $\ge$ $\frac{19}{4}$ that is [$\frac{19}{4}$, infy)