# How do you find the vertex of y= 3x^2 +12x-6?

Apr 24, 2018

$\text{vertex } = \left(- 2 , - 18\right)$

#### Explanation:

$\text{Given the quadratic in "color(blue)"standard form}$

•color(white)(x)y=ax^2+bx+c;a!=0

$\text{then the x-coordinate of the vertex can be found using}$

•color(white)(x)x_(color(red)"vertex")=-b/(2a)

$y = 3 {x}^{2} + 12 x - 6 \text{ with } a = 3 , b = 12 , c = - 6$

$\Rightarrow {x}_{\text{vertex}} = - 12 \left(6\right) = - 2$

$\text{substitute this value into the equation for y}$

${y}_{\text{vertex}} = 3 {\left(- 2\right)}^{2} + 12 \left(- 2\right) - 6 = - 18$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 2 , - 18\right)$