# How do you find the vertex of y=3x^2 - 12x - 2?

Jul 19, 2018

The vertex is at $\left(2 , - 14\right)$.

#### Explanation:

To find the vertex of a standard quadratic equation $y = a {x}^{2} + b x + c$, we first use the formula $- \frac{b}{2 a}$ to find the $x$ value of the vertex, or ${x}_{v}$. We know that $a = 3$ and $b = - 12$:
$x = - \frac{b}{2 a} = \frac{- \left(- 12\right)}{2 \left(3\right)} = \frac{12}{6} = 2$

To find the $y$ value of the vertex we simply plug in the $x$ value back into the equation and solve for $y$:
$y = 3 {x}^{2} - 12 x - 2$

$y = 3 {\left(2\right)}^{2} - 12 \left(2\right) - 2$

$y = 3 \left(4\right) - 24 - 2$

$y = 12 - 24 - 2$

$y = - 14$

Therefore, the vertex is at $\left(2 , - 14\right)$.

Hope this helps!