How do you find the axis of symmetry, and the maximum or minimum value of the function #y=x^{2}-6x+4#?

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Answer 1 · 2017-04-04T07:26:48

The minimum value is at #(3,-5)#

The equation of this parabola is in the form #y = ax^2 +bx+c#

#y = x^2 -6x+4" "rarr" "a=1," " b=-6 and c =4#

The axis of symmetry is found from #x= (-b)/(2a)#

#x= (-(-6))/(2xx1) = 6/2=3#

The Turning Point is the maximum or minimum value and it lies on the axis of symmetry, so you have the #x#-coordinate

If #x=3#, substitute to find #y#.

#y = (3)^2 -6(3)+4 = 9-18+4#

#y = -5#

In this case the parabola opens upwards (#a >0#, ie positive), therefore the Turning Point is a minimum value.

#(3,-5)#