What is the the vertex of #y=x^2+7x +12 #?

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Answer 1 · 2016-01-29T07:44:42

#(-7/2,-1/4)#

Re-express in vertex form by completing the square:

#y=x^2+7x+12#

#=x^2+7x+(7/2)^2-(7/2)^2+12#

#=(x+7/2)^2-49/4+48/4#

#=1(x-(-7/2))^2+(-1/4)#

The equation:

#y = 1(x-(-7/2))^2+(-1/4)#

is in vertex form:

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

with multiplier #a=1# and vertex #(h,k) = (-7/2,-1/4)#