What is the vertex of #y=x^2-6x+8#?

1 Answer
Tony B
May 23, 2016

#color(blue)("Vertex"->(x,y)->(3,-1)#

Explanation:

The given equation is in the format #y=a(x^2+b/ax)+c#

In your case #a=1#

The following process is part way to completing the square

#color(blue)(x_("vertex")=(-1/2)xxb/a -> (-1/2)xx(-6) = +3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute #x=+3# in the original equation to determine #y_("vertex")#

#color(blue)(y_("vertex")=(3)^2-6(3)+8 = -1)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Vertex"->(x,y)->(3,-1)#

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