# How do you write y=x^2-8x+20 into vertex form?

Apr 11, 2018

$y = {\left(x - 4\right)}^{2} + 4$

#### Explanation:

$y = \left[{x}^{2} - 8 x\right] + 20$
$y = \left[{\left(x - 4\right)}^{2} - 16\right] + 20$
$y = {\left(x - 4\right)}^{2} - 16 + 20$
$y = {\left(x - 4\right)}^{2} + 4$

Apr 11, 2018

$y = {\left(x - 4\right)}^{2} + 4$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the vertex and a }$
$\text{is a multiplier}$

$\text{to obtain this form use the method of "color(blue)"completing the square}$

• " the coefficient of the "x^2" term must be 1 which it is"

• " add/subtract "(1/2"coefficient of the x-term")^2" to"
${x}^{2} - 8 x$

$\Rightarrow y = {x}^{2} + 2 \left(- 4\right) x \textcolor{red}{+ 16} \textcolor{red}{- 16} + 20$

$\Rightarrow y = {\left(x - 4\right)}^{2} + 4 \leftarrow \textcolor{red}{\text{in vertex form}}$