How do you find the vertex of a parabola #y = x^2 - 6x + 10#?

1 Answer
Alan P.
Jun 30, 2015

The vertex is at #(3,1)#

Explanation:

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

Converting #y = x^2-6x+10# into vertex form:
#color(white)("XXXX")#Note #m=1# and we can continue with the rest of the conversion.
#color(white)("XXXX")#Complete the square
#color(white)("XXXX")##color(white)("XXXX")##y= x^2-6x+9 + 1#
#color(white)("XXXX")##color(white)("XXXX")##y = (x-3)+1#

and we can simply read off the vertex coordinates.

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