# How do you write y=2x^2-9x-5 in vertex form?

Sep 7, 2017

$y = 2 {\left(x - \frac{9}{4}\right)}^{2} - \frac{121}{8}$

#### 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.

$\text{to obtain this form "color(blue)"complete the square}$

$y = 2 \left({x}^{2} - \frac{9}{2} x\right) - 5 \leftarrow \text{ coefficient of "x^2" equal to 1}$

$\textcolor{w h i t e}{y} = 2 \left({x}^{2} + 2 \left(- \frac{9}{4}\right) x + \frac{81}{16} - \frac{81}{16}\right) - 5$

$\textcolor{w h i t e}{y} = 2 {\left(x - \frac{9}{4}\right)}^{2} - \frac{81}{8} - 5$

$\textcolor{w h i t e}{y} = 2 {\left(x - \frac{9}{4}\right)}^{2} - \frac{121}{8}$