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

Apr 20, 2017

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

#### Explanation:

The equation of a parabola in $\textcolor{b l u e}{\text{vertex form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where (h ,k) are the coordinates of the vertex and a is a constant.

$\text{Rearrange " y=x^2-2x" into this form}$

$\text{using the method of "color(blue)"completing the square}$

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

$\Rightarrow y = {\left(x - 1\right)}^{2} - 1 \leftarrow \textcolor{red}{\text{ in vertex form}}$