# How do you write the Vertex form equation of the parabola  y=x^2+4x+1?

Feb 13, 2016

# y = (x+2)^2 - 3

#### Explanation:

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

the equation here $y = {x}^{2} + 4 x + 1$

gives by comparison : a = 1 , b =4 and c = 1

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 = $- \frac{b}{2 a} = - \frac{4}{2} = - 2$

and y-coord $= {\left(- 2\right)}^{2} + 4 \left(- 2\right) + 1 = 4 - 8 + 1 = - 3$

hence (h , k) = ( -2 , -3 ) and a = 1

equation in vertex form is : $y = {\left(x + 2\right)}^{2} - 3$