How do you write f(x) = x^2 - 3x + 2 into vertex form?

May 28, 2015

The vertex form of a parabolic equation is of the form:
$f \left(x\right) = {\left(x - a\right)}^{2} + b$ where the vertex is located at $\left(a , b\right)$

Conversion of a parabolic equation to vertex form usually involves completion of the square methods.

Given $f \left(x\right) = {x}^{2} - 3 x + 2$

$f \left(x\right) = {x}^{2} - 3 x + {\left(\frac{3}{2}\right)}^{2} + 2 - {\left(\frac{3}{2}\right)}^{2}$

$= {\left(x - \frac{3}{2}\right)}^{2} - \frac{1}{4}$
or in complete vertex form
$= {\left(x - \frac{3}{2}\right)}^{2} + \left(- \frac{1}{4}\right)$ with the vertex at $\left(\frac{3}{2} , - \frac{1}{4}\right)$