# What is the vertex form of  y = 2x^2 + 8x − 3 ?

Dec 23, 2017

$y = 2 {\left(x + 2\right)}^{2} - 11$

#### Explanation:

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

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

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

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

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

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

• " add/subtract "(1/2"coefficient of x-term")^2" to"
${x}^{2} + 4 x$

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

$\textcolor{w h i t e}{y} = 2 {\left(x + 2\right)}^{2} - 8 - 3$

$\Rightarrow y = 2 {\left(x + 2\right)}^{2} - 11 \leftarrow \textcolor{red}{\text{in vertex form}}$