# What is the vertex form of y= 5x^2-9x-2 ?

Mar 16, 2018

$5 {\left(x - \frac{9}{10}\right)}^{2} - \frac{121}{20}$

#### Explanation:

We have to write the above in the form $a {\left(x - h\right)}^{2} + k$

We have:

$5 {x}^{2} - 9 x - 2$

$5 \left({x}^{2} - \frac{9}{5} x\right) - 2$

Completing the square incide the bracket,

$5 \left({x}^{2} - \frac{9}{5} x + \frac{81}{100}\right) - 2 - \frac{81}{20}$

$5 {\left(x - \frac{9}{10}\right)}^{2} - \frac{121}{20}$

This is in the above form.

By the way, the vertex is at $\left(\frac{9}{10} , - \frac{121}{20}\right)$