What is the vertex form of #f(x) = x^2+4x+6#?

1 Answer
Feb 13, 2016

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

Explanation:

the standard form of a quadratic function is #y = ax^2 + bx + c#

here # f(x) = x^2 + 4x + 6#

and by comparison : a = 1 , b = 4 and c = 6

in vertex form the equation is: # y = a(x-h)^2 + k #

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

the x-coord of vertex # = -b/(2a) = -4/2 = - 2 #

and y-coord. =#(-2)^2 + 4(-2) +6 = 4 - 8 + 6 = 2#

now (h , k) =(-2 , 2) and a = 1

# rArr y = (x+2)^2 + 2 #