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

Dec 4, 2017

$y = {\left(x - \frac{15}{64}\right)}^{2} + \frac{339}{1024}$

#### Explanation:

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

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

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

$\text{given the equation in standard form } a {x}^{2} + b x + c$

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

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

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

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

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{- \frac{3}{8}}{\frac{8}{5}} = \frac{15}{64}$

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

$y = \frac{4}{5} {\left(\frac{15}{64}\right)}^{2} - \frac{3}{8} \left(\frac{15}{64}\right) + \frac{3}{8} = \frac{339}{1024}$

$\Rightarrow y = {\left(x - \frac{15}{64}\right)}^{2} + \frac{339}{1024} \leftarrow \textcolor{red}{\text{in vertex form}}$