What is the vertex form of #y= x^2 + 7x – 6 #?

1 Answer
Alan P.
Aug 31, 2017

#y=color(green)1(x-color(red)(""(-7/2)))^2+color(blue)(""(-25/4))#
with vertex at
#color(white)("XXX")(color(red)(-7/2),color(blue)(-25/4))#

Explanation:

Given
#color(white)("XXX")y=x^2+7x+6#

Complete the square:
#color(white)("XXX")y=x^2+7xcolor(magenta)(""+(7/2)^2)+6color(magenta)(-(7/2)^2)#

#color(white)("XXX")y=(x+7/2)^2+24/4-49/4#

#color(white)("XXX")y=(x+7/2)^2-25/4#

Some instructors might accept this as a solution,
but in its complete form, the vertex form should look like:
#color(white)("XXX")y=color(green)m(x-color(red)a)^2+color(blue)b#
in order to easily read the vertex coordinates.

You should have no difficulty in converting to the form provided in the "Answer".
#color(green)m# must be #color(green)(1)#
converting #(x+7/2)# gives #(x-color(red)(""(-7/2)))#
and #-25/4# is equivalent to #color(blue)(+(-25/4))#

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