# How do you write the vertex form equation of the parabola 3x^2+30x-y+71=0?

Jan 22, 2018

$y = 3 {\left(x + 5\right)}^{2} - 4$

#### Explanation:

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

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

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

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

$\text{express as } y = 3 {x}^{2} + 30 x + 71$

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

$\Rightarrow y = 3 \left({x}^{2} + 10 x + \frac{71}{3}\right)$

• " add/subtract "(1/2"coefficient of x-term")^2" to"
${x}^{2} + 10 x$

$\Rightarrow y = 3 \left({x}^{2} + 2 \left(5\right) x \textcolor{red}{+ 25} \textcolor{red}{- 25} + \frac{71}{3}\right)$

$\textcolor{w h i t e}{\Rightarrow y} = 3 {\left(x + 5\right)}^{2} + 3 \left(- \frac{75}{3} + \frac{71}{3}\right)$

$\textcolor{w h i t e}{\Rightarrow y} = 3 {\left(x + 5\right)}^{2} - 4 \leftarrow \textcolor{red}{\text{in vertex form}}$