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 #
