# How do you write the vertex form equation of the parabola y=x^2+4x-5?

Feb 23, 2016

$y = {\left(x + 2\right)}^{2} - 9$

#### Explanation:

The standard form of a quadratic function is $y = a {x}^{2} + b x + c$

The function $y = {x}^{2} + 4 x - 5 \text{ is in this form }$

and by comparison a = 1 , b = 4 and c = -5

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

where (h , k ) are the coords of the vertex.

x-coord of vertex (h) $= \frac{- b}{2 a} = \frac{- 4}{2} = - 2$

and y-coord (k) = ${\left(- 2\right)}^{2} + 4 \left(- 2\right) - 5 = 4 - 8 - 5 = - 9$

hence (h , k ) = (-2 , -9) and a = 1

$\Rightarrow y = {\left(x + 2\right)}^{2} - 9 \text{ is vertex form of equation }$