# What is the vertex form of y= 6x^2 - 4x - 24 ?

Jul 2, 2016

$y = 6 {\left(x - \frac{1}{3}\right)}^{2} - 24 \frac{2}{3}$

The vertex is at $\left(\frac{1}{3} . - 24 \frac{2}{3}\right)$

#### Explanation:

If you write a quadratic in the form

$a {\left(x + b\right)}^{2} + c$, then the vertex is $\left(- b , c\right)$

Use the process of completing the square to get this form:

$y = 6 {x}^{2} - 4 x - 24$

Factor out the 6 to make $6 {x}^{2}$ into "x^2

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

Find half of $\frac{2}{3}$ .................................2/3 ÷ 2 = 1/3

square it....... ${\left(\frac{1}{3}\right)}^{2}$ and add it and subtract it.

$y = 6 \left[{x}^{2} - \frac{2 x}{3} \textcolor{red}{+ {\left(\frac{1}{3}\right)}^{2}} - 4 \textcolor{red}{- {\left(\frac{1}{3}\right)}^{2}}\right]$

Write the first 3 terms as the square of a binomial

$y = 6 \left[{\left(x - \frac{1}{3}\right)}^{2} - 4 \frac{1}{9}\right]$

Multiply the 6 into the bracket to get the vertex form.

$y = 6 {\left(x - \frac{1}{3}\right)}^{2} - 24 \frac{2}{3}$

The vertex is at $\left(\frac{1}{3} . - 24 \frac{2}{3}\right)$