# What is the vertex form of y = 12x^2 -4x + 6?

Apr 23, 2017

$y = 12 {\left(x - \frac{1}{6}\right)}^{2} + \frac{17}{3}$

#### Explanation:

$y = 12 {x}^{2} - 4 x + 6$

Factor out the $a$ value to make the numbers smaller and easier to use:
$y = 12 \left[{x}^{2} - \frac{1}{3} x + \frac{1}{2}\right]$

Rewrite what's inside the brackets by completing the square
$y = 12 \left[{\left(x - \frac{1}{6}\right)}^{2} + \left(\frac{1}{2} - \frac{1}{36}\right)\right]$

$y = 12 \left[{\left(x - \frac{1}{6}\right)}^{2} + \frac{17}{36}\right]$

Finally distribute the 12 back
$y = 12 {\left(x - \frac{1}{6}\right)}^{2} + \frac{17}{3}$