# How do you write the Vertex form equation of the parabola y=x^2-2x+1?

Feb 19, 2016

$y = 1 {\left(x - 1\right)}^{2} + 0$

#### Explanation:

The general vertex form for a parabola is
$\textcolor{w h i t e}{\text{XXX}} y = m {\left(x - a\right)}^{2} + b$
for a parabola with vertex at $\left(a , b\right)$.

Given:
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} - 2 x + 1$
and re-writing the expression on the left as a squared binomial:
$\textcolor{w h i t e}{\text{XXX}} y = {\left(x - 1\right)}^{2}$
Note that some teachers would accept this as a final answer;
however to be technically complete we should include values for the $m$ and $b$ elements:
$\textcolor{w h i t e}{\text{XXX}} y = 1 {\left(x - 1\right)}^{2} + 0$