# What is the the vertex of y = -12x^2 - 2x - 6?

Feb 29, 2016

$\left(- \frac{1}{12} , - \frac{71}{12}\right)$

#### Explanation:

Write the equation in vertex form as follows:

y= $- 12 \left({x}^{2} + \frac{x}{6}\right) - 6$

= $- 12 \left({x}^{2} + \frac{x}{6} + \frac{1}{144} - \frac{1}{144}\right) - 6$

=$- 12 {\left(x + \frac{1}{12}\right)}^{2} - 6 + \frac{12}{144}$

=$- 12 {\left(x + \frac{1}{12}\right)}^{2} - \frac{71}{12}$

The vertex is therefore $\left(- \frac{1}{12} , - \frac{71}{12}\right)$