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

##### 1 Answer

Feb 13, 2016

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

#### Explanation:

the standard form of a quadratic is

#y = ax^2 + bx + c# the equation here

# y = x^2 + 4x + 1 # gives by comparison : a = 1 , b =4 and c = 1

the vertex form of the equation is

# y =a (x - h )^2 + k # where (h , k ) are the coords of the vertex.

x-coord of vertex =

# -b/(2a) = -4/2 = -2 # and y-coord

# = (-2)^2 +4(-2) + 1 = 4 - 8 + 1 = -3# hence (h , k) = ( -2 , -3 ) and a = 1

equation in vertex form is :

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