# What is the vertex form of y= 4x^2 -12x + 9 ?

Jun 17, 2017

$y = 4 {\left(x - \frac{3}{2}\right)}^{2}$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where ( h , k ) are the coordinates of the vertex and a is a constant.

$\text{for a parabola in standard form } y = a {x}^{2} + b x + c$

"the x-coordinate of the vertex is " x_(color(red)"vertex")=-b/(2a)

$y = 4 {x}^{2} - 12 x + 9 \text{ is in standard form}$

$\text{with } a = 4 , b = - 12 , c = 9$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{- 12}{8} = \frac{3}{2}$

$\text{substitute this value into function for y-coordinate}$

$y = 4 {\left(\frac{3}{2}\right)}^{2} - 12 \left(\frac{3}{2}\right) + 9 = 9 - 18 + 9 = 0$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(\frac{3}{2} , 0\right)$

$\Rightarrow y = 4 {\left(x - \frac{3}{2}\right)}^{2} \leftarrow \textcolor{red}{\text{ in vertex form}}$