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

Dec 31, 2015

$y = {\left(x - \left(- 1\right)\right)}^{2} + \left(- 5\right)$

#### Explanation:

The vertex form of a quadratic equation $y = a {x}^{2} + b x + c$ is
$y = a {\left(x - h\right)}^{2} + k$ where $\left(h , k\right)$ is the vertex.

To find the vertex form, we use a process called completing the square

For this particular equation:
$y = {x}^{2} + 2 x - 4$

$\implies y = \left({x}^{2} + 2 x + 1\right) - 1 - 4$

$\implies y = {\left(x + 1\right)}^{2} - 5$

$\therefore y = {\left(x - \left(- 1\right)\right)}^{2} + \left(- 5\right)$

Thus we have the vertex form

$y = {\left(x - \left(- 1\right)\right)}^{2} + \left(- 5\right)$ and the vertex is at $\left(- 1 , - 5\right)$