# What is the vertex form of y= - 3x^2 +7x - 15 ?

Nov 15, 2017

$y = - 3 {\left(x - \frac{7}{6}\right)}^{2} - \frac{131}{12}$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the vertex and a}$
$\text{is a multiplier}$

$\text{to obtain this form use the method of "color(blue)"completing the square}$

• " coefficient of "x^2" term must be 1"

$\Rightarrow y = - 3 \left({x}^{2} - \frac{7}{3} x + 5\right)$

• " add/subtract "(1/2"coefficient of x-term")^2

$\Rightarrow y = - 3 \left({x}^{2} + 2 \left(- \frac{7}{6}\right) x \textcolor{red}{+ \frac{49}{36}} \textcolor{red}{- \frac{49}{36}} + 5\right)$

$\textcolor{w h i t e}{\Rightarrow y} = - 3 {\left(x - \frac{7}{6}\right)}^{2} - 3 \left(- \frac{49}{6} + 5\right)$

$\textcolor{w h i t e}{\Rightarrow y} = - 3 {\left(x - \frac{7}{6}\right)}^{2} - \frac{131}{12} \leftarrow \textcolor{red}{\text{in vertex form}}$