# What is the vertex form of y= 12x^2-14x-6 ?

Apr 8, 2017

$y = 12 {\left(x - \frac{7}{12}\right)}^{2} - \frac{121}{12}$

#### Explanation:

The equation of a parabola in $\textcolor{b l u e}{\text{vertex form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where (h ,k) are the coordinates of the vertex and a is constant.

$\text{Rearrange " y=12x^2-14x-6" into this form}$

$\text{Using the method of "color(blue)"completing the square}$

$y = 12 \left({x}^{2} - \frac{7}{6} x - \frac{1}{2}\right) \leftarrow \text{ coefficient of " x^2" is unity}$

$y = 12 \left[\left({x}^{2} - \frac{7}{6} x \textcolor{red}{+ \frac{49}{144}}\right) \textcolor{red}{- \frac{49}{144}} - \frac{1}{2}\right]$

$\textcolor{w h i t e}{y} = 12 \left[{\left(x - \frac{7}{12}\right)}^{2} - \frac{121}{144}\right]$

$\Rightarrow y = 12 {\left(x - \frac{7}{12}\right)}^{2} - \frac{121}{12} \leftarrow \textcolor{red}{\text{ in vertex form}}$