# What is the vertex form of  f(x) = -5x^2-x-12 ?

$f \left(x\right) = - 5 {\left(x + \frac{1}{10}\right)}^{2} - \frac{239}{20}$
$f \left(x\right) = - 5 \left({x}^{2} + \frac{1}{5} x\right) - 12$
$= - 5 \left({x}^{2} + \frac{1}{5} x + \frac{1}{100}\right) - 12 + \frac{1}{20}$
$= - 5 {\left(x + \frac{1}{10}\right)}^{2} - \frac{239}{20}$