How do you identify the important parts of #g(x)=-x^2+12x-36# to graph it?

1 Answer
Nallasivam V
Sep 30, 2015

Its vertex is #(6,0)#
Axis of symmetry is #x=6#
Since co-efficient of x is #-1#, the curve is concave downwards.
It has a maxima at #(6,0)#

Explanation:

#g(x)=−x^2+12x−36#

#x=(-b)/(2a)=(-12)/(2 xx (-1))=(-12)/(-2)=6#

At #x=6; f(x) =-(6^2)+12(6)-36#
# f(x) =-36+72-36=-72+72=0#

Its vertex is #(6,0)#
Axis of symmetry is #x=6#
Since co-efficient of x is #-1#, the curve is concave downwards.

It has a maxima at #(6,0)#

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