# What is the vertex form of y=2x^2+4x-5?

Jul 26, 2016

y=color(green)(2)(x-color(red)(""(-1)))^2+color(blue)(""(-8))

#### Explanation:

Given:
$\textcolor{w h i t e}{\text{XXX}} y = 2 {x}^{2} + 4 x - 5$

Remember that the vertex form is
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{b l u e}{b}$
with vertex at $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$

Extracting the the $\textcolor{g r e e n}{m}$ factor from the given equation
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{2} \left({x}^{2} + 2 x\right) - 5$

Complete the square
color(white)("XXX")y=color(green)(2)(x^2+2xcolor(purple)(+1))-5-color(green)(2)*color(purple)(1))

Rewrite with a squared binomial and simplified constant
$\textcolor{w h i t e}{\text{XXX")y=color(green)(2)(x-color(red)(""(-1)))^2+color(blue)(} \left(- 8\right)}$
which is the vertex form with vertex at $\left(\textcolor{red}{- 1} , \textcolor{b l u e}{- 8}\right)$

Here is a graph of the original equation for verification purposes:
graph{2x^2+4x-5 [-10.83, 11.67, -10.08, 1.17]}