How do you find the vertex of a parabola #y=2x^2 -12x+23#?

1 Answer
Alan P.
Jul 8, 2015

The easiest way is (probably) to convert the given equation into vertex form.
The vertex is at #(3,5)#

Explanation:

Vertex form of a parabola is
#color(white)("XXXX")##y =m(x-a)^2+b# with its vertex as #(a,b)#

#y = 2x^2-12x+23#
#color(white)("XXXX")#extract the #m#
#y = 2(x^2-6x) +23#
#color(white)("XXXX")#complete the square
#y = 2(x^2-6x+9) + 23 -2(9)#
#color(white)("XXXX")#simplify into vertex form
#y=2(x-3)^2 + 5#

Since this is in vertex form, we can read the vertex directly from the equation as #(3,5)#

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