# What is y = x^2-16x+40 written in vertex form?

Mar 26, 2018

$y = {\left(x - 8\right)}^{2} - 24$

#### Explanation:

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

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

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

$\text{Give the equation in "color(blue)"standard form}$

•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0

$\text{then the x-coordinate of the vertex is}$

•color(white)(x)x_(color(red)"vertex")=-b/(2a)

$y = {x}^{2} - 16 x + 40 \text{ is in standard form}$

$\text{with "a=1,b=-16" and } c = 40$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{- 16}{2} = 8$

$\text{substitute "x=8" into the equation for y-coordinate}$

${y}_{\textcolor{red}{\text{vertex}}} = {8}^{2} - \left(16 \times 8\right) + 40 = - 24$

$\Rightarrow \left(h , k\right) = \left(8 , - 24\right)$

$\Rightarrow y = {\left(x - 8\right)}^{2} - 24 \leftarrow \textcolor{red}{\text{in vertex form}}$