How do you find the axis of symmetry, and the maximum or minimum value of the function #y = x^2 - 6x + 7#?

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Answer 1 · 2017-05-29T12:55:23

The axis of symmetry is #x=3# and the minimum value is #=-2# at the point #(3,-2)#

We complete the square by adding half the coefficient of #x# to the square and substract this value

#(-6/2)^2=9#

#y=x^2-6x+7#

#y=x^2-6x+9+7-9#

#y=(x-3)^2-2#

The axis of symmetry is #x=3#

As the coefficient of #x^2# is #1>0#, the minimum value is when

#x=3#

#y(3)=-2=-2#

graph{(y-x^2+6x-7)(y-1000(x-3))((x-3)^2+(y+2)^2-0.01)=0 [-7.9, 7.9, -3.95, 3.95]}