# How do you find the vertex of a parabola y=x^2+2x-1?

##### 1 Answer
Apr 10, 2015

The vertex of a parabola occurs when its derivative is equal to $0$

$y = {x}^{2} + 2 x - 1$

$y ' = 2 x + 2 = 0$ for the vertex
that is
$x = - 1$ at the vertex

Substituting $x = - 1$ back into the original equation gives
$y = {\left(- 1\right)}^{2} + 2 \left(- 1\right) - 1$
$= 1 - 2 - 1 = - 3$

So the vertex of the parabola occurs at $\left(- 1 , - 3\right)$