How do you find the VERTEX of a parabola #y=-3x^2+12x-9#?

1 Answer
Alan P.
Jul 22, 2015

Re-write the given equation in "vertex form" to get:
#color(white)("XXXX")#vertex at #(2,3)#

Explanation:

The general "vertex form" for a parabola is
#color(white)("XXXX")##y=m(x-a)^2+b#
#color(white)("XXXX")##color(white)("XXXX")#with a vertex at #(a,b)#

Given #y = -3x^2+12x-9#

Extract #m#
#color(white)("XXXX")##y = (-3)(x^2-4x) -9#

Complete the square:
#color(white)("XXXX")##y = (-3)(x^2-4x+4) - 9 +3(4)#

#color(white)("XXXX")##y = (-3)(x-2)^2 +3#
#color(white)("XXXX")##color(white)("XXXX")#which is the vertex form
#color(white)("XXXX")##color(white)("XXXX")#with vertex at #(2,3)#

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