# What is the vertex form of 7y=(2x -8)(4x - 5) ?

Jan 15, 2018

$y = \frac{8}{7} {\left(x - \frac{21}{8}\right)}^{2} - \frac{121}{56}$

#### Explanation:

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

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

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

$\text{expand the factors}$

$\Rightarrow 7 y = 8 {x}^{2} - 42 x + 40$

$\text{to express in vertex form use "color(blue)"completing the square}$

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

$\Rightarrow 7 y = 8 \left({x}^{2} - \frac{21}{4} + 5\right)$

• " add/subtract "(1/2"coefficient of x-term")^2" to "
${x}^{2} - \frac{21}{4} x$

$7 y = 8 \left({x}^{2} + 2 \left(- \frac{21}{8}\right) x \textcolor{red}{+ \frac{441}{64}} \textcolor{red}{- \frac{441}{64}} + 5\right)$

$\textcolor{w h i t e}{7 y} = 8 {\left(x - \frac{21}{8}\right)}^{2} + 8 \left(- \frac{441}{64} + 5\right)$

$\textcolor{w h i t e}{7 y} = 8 {\left(x - \frac{21}{8}\right)}^{2} - \frac{121}{8}$

$\Rightarrow y = \frac{8}{7} {\left(x - \frac{21}{8}\right)}^{2} - \frac{121}{56}$