# What is the vertex form of y=-5/8x^2+7/4x +2/3?

Feb 8, 2018

$y = - \frac{5}{8} {\left(x - \frac{7}{5}\right)}^{2} + \frac{227}{120}$

#### Explanation:

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

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

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

$\text{given the equation in standard form}$

•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)

$y = - \frac{5}{8} {x}^{2} + \frac{7}{4} x + \frac{2}{3} \text{ is in standard form}$

$\text{with "a=-5/8,b=7/4" and } c = \frac{2}{3}$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{\frac{7}{4}}{- \frac{5}{4}} = \frac{7}{5}$

$\text{substitute this value into the equation for y}$

${y}_{\textcolor{red}{\text{vertex}}} = - \frac{5}{8} {\left(\frac{7}{5}\right)}^{2} + \frac{7}{4} \left(\frac{7}{5}\right) + \frac{2}{3} = \frac{227}{120}$

$\Rightarrow y = - \frac{5}{8} {\left(x - \frac{7}{5}\right)}^{2} + \frac{227}{120} \leftarrow \textcolor{b l u e}{\text{in vertex form}}$