# What is the vertex of  y= 2(x-5)^2-5x^2-x-1?

Jan 20, 2016

The vertex is $\left(- \frac{7}{2} , \frac{343}{4}\right)$

#### Explanation:

First expand the equation to get rid of the brackets and into standard form. The expression can then be rearranged into vertex to identify the vertex.

$y = 2 \left({x}^{2} - 10 x + 25\right) - 5 {x}^{2} - x - 1$
$y = - 3 {x}^{2} - 21 x + 49$
$y = - 3 \left({x}^{2} + 7 x\right) + 49$

$y = - 3 {\left(x + \frac{7}{2}\right)}^{2} + \frac{147}{4} + 49$
$y = - 3 {\left(x + \frac{7}{2}\right)}^{2} + \frac{343}{4}$

The vertex is $\left(- \frac{7}{2} , \frac{343}{4}\right)$