# What is the vertex form of  f(x) = -5x^2-4x+9 ?

$x = - \frac{b}{2 a} = \frac{4}{-} 10 = - \frac{2}{5}$
$y \left(- \frac{2}{5}\right) = - 5 \left(\frac{4}{25}\right) + 4 \left(\frac{2}{5}\right) + 9 = - \frac{4}{5} + \frac{8}{5} + 9 = \frac{49}{5}$
Vertex $\left(- \frac{2}{5} , \frac{49}{5}\right)$
$f \left(x\right) = - 5 {\left(x + \frac{2}{5}\right)}^{2} + \frac{49}{5}$