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

Feb 1, 2016

vertex at $\left(- 2 , - 9\right)$

#### Explanation:

Often the simplest way to do this is to convert the given equation into "vertex form":
$\textcolor{w h i t e}{\text{XXX}} y = {\left(x - a\right)}^{2} + b$ with its vertex at $\left(a , b\right)$

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

Completing the square:
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} + 4 x \textcolor{b l u e}{+ 4} - 5 \textcolor{b l u e}{- 4}$

Re-writing as a squared binomial and simplified constant
$\textcolor{w h i t e}{\text{XXX}} y = {\left(x + 2\right)}^{2} - 9$

Modifying signs into explicit vertex form:
$\textcolor{w h i t e}{\text{XXX}} y = {\left(x - \left(- 2\right)\right)}^{2} + \left(- 9\right)$

If you have access to some graphing software, it can help verify that the answer is reasonable by graphing the original equation.
graph{x^2+4x-5 [-8.91, 11.09, -9.59, 0.41]}