What is the vertex form of #7y = 3x^2+2x+1#?

1 Answer
Feb 15, 2018

Vertex form is:

#y = 3/7(x+1/3)^2+2/21#

or if you prefer:

#y = 3/7(x-(-1/3))^2+2/21#

Explanation:

Given:

#7y = 3x^2+2x+1#

Divide both sides by #7# then complete the square:

#y = 3/7x^2+2/7x+1/7#

#color(white)(y) = 3/7(x^2+2/3x+1/9+2/9)#

#color(white)(y) = 3/7(x+1/3)^2+2/21#

The equation:

#y = 3/7(x+1/3)^2+2/21#

is pretty much vertex form:

#y = a(x-h)^2+k#

with multiplier #a=3/7# and vertex #(h, k) = (-1/3, 2/21)#

Strictly speaking, we could write:

#y = 3/7(x-(-1/3))^2+2/21#

just to make the #h# value clear.