# What is the vertex form of  y = 3x^2 + 9x − 4 ?

$x = - \frac{b}{2 a} = - \frac{9}{6} = - \frac{3}{2.}$
$y \left(- \frac{3}{2}\right) = 3 \left(\frac{9}{4}\right) - 9 \left(\frac{3}{2}\right) - 4 = \frac{27}{4} - \frac{27}{2} - 4 = - \frac{43}{4}$
Vertex form: $y = {\left(x + \frac{3}{2}\right)}^{2} - \frac{43}{4}$