# What is the vertex form of y=2x^2 + 4x + 46 ?

Apr 3, 2017

$y = 2 {\left(x + 1\right)}^{2} + 44$

#### 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 a constant.

We can obtain vertex form by $\textcolor{b l u e}{\text{completing the square}}$

$y = 2 \left({x}^{2} + 2 x + 23\right)$

$\textcolor{w h i t e}{x} = 2 \left({x}^{2} + 2 x \textcolor{red}{+ 1} \textcolor{red}{- 1} + 23\right)$

$\textcolor{w h i t e}{x} = 2 \left({\left(x + 1\right)}^{2} + 22\right)$

$\Rightarrow y = 2 {\left(x + 1\right)}^{2} + 44 \leftarrow \textcolor{red}{\text{ in vertex form}}$