# What is the vertex form of y=x^2-2x+6?

Mar 2, 2018

In vertex form, the parabola's equation is $y = {\left(x - 1\right)}^{2} + 5$.

#### Explanation:

To convert a parabola in standard form to vertex form, you have to make a squared binomial term (i.e. ${\left(x - 1\right)}^{2}$ or ${\left(x + 6\right)}^{2}$).

These squared binomial terms -- take ${\left(x - 1\right)}^{2}$, for example -- (almost) always expand to have ${x}^{2}$, $x$, and constant terms. ${\left(x - 1\right)}^{2}$ expands to be ${x}^{2} - 2 x + 1$.

In our parabola:

$y = {x}^{2} - 2 x + 6$

We have a part that looks similar to the expression we wrote before: ${x}^{2} - 2 x + 1$. If we rewrite our parabola, we can "undo" this squared binomial term, like this:

$y = {x}^{2} - 2 x + 6$

$\textcolor{w h i t e}{y} = \textcolor{red}{{x}^{2} - 2 x + 1} + 5$

$\textcolor{w h i t e}{y} = \textcolor{red}{{\left(x - 1\right)}^{2}} + 5$

This is our parabola in vertex form. Here's its graph:

graph{(x-1)^2+5 [-12, 13.7, 0, 13.12]}