# What is the vertex form of y = 6x^2 - 24x + 16?

Jul 8, 2018

$y = 6 {\left(x - 2\right)}^{2} - 8$

#### Explanation:

We have

$y = 6 {x}^{2} - 24 x + 16$
and this is

$y = 6 \left({x}^{2} - 4 x + \frac{16}{6}\right)$
$y = 6 \left({x}^{2} - 4 x + \frac{8}{3}\right)$
now we complete the square

$y = 6 \left({x}^{2} - 4 x + 4 + \frac{8}{3} - 4\right)$

we use that

${x}^{2} - 4 x + 4 = {\left(x - 2\right)}^{2}$
and

$\frac{8}{3} - 4 = \frac{8}{3} - \frac{12}{3} = - \frac{4}{3}$

so we get

$y = 6 {\left(x - 2\right)}^{2} - 6 \cdot \frac{4}{3}$

the result is given by

$y = 6 {\left(x - 2\right)}^{2} - 8$
and this is the vertex form