# What is the vertex of # y= -12x^2-4x-2?

Apr 25, 2017

The vertex is at $\left(- \frac{1}{6} , - \frac{5}{3}\right)$

#### Explanation:

$y = - 12 {x}^{2} - 4 x - 2$. Comparing with standard equation $a {x}^{2} + b x + c$ we get $a = - 12 , b = - 4 , c = - 2$
$x$ co-ordinate of vertex is $- \frac{b}{2 a} = - \frac{4}{2 \cdot - 12} = - \frac{1}{6}$

Then, $y$ co-ordinate of vertex is $y = - 12 {\left(- \frac{1}{6}\right)}^{2} - 4 \left(- \frac{1}{6}\right) - 2 = - \frac{5}{3}$
The vertex is at $\left(- \frac{1}{6} , - \frac{5}{3}\right)$ graph{-12x^2-4x-2 [-20, 20, -10, 10]}