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

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Answer 1 · 2017-06-07T00:31:58

The axis of symmetry is #x=3#.

The minimum (vertex) is #(3,-7)#.

#y=x^2-6x+2# is a quadratic equation in the form: #ax^2-bx+c#, where #a=1#, #b=-6#, and #c=2#.

The axis of symmetry:

#x=(-b)/(2a)#

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

Simplify.

#x=6/2=3#

#x=3#

The vertex is the maximum or minimum of the parabola.

If #a>0#, the parabola will open upwards, and the vertex will be a minimum.

If #a<0#, the parabola will open downward, and the vertex will be a maximum.

In the current equation #>0# so the parabola so the vertex is the minimum and the parabola will open upward.

With a standard equation, substitute the value for #x# and solve for #y#. The point #(x,y)# is the vertex.

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

#y=3^2-6(3)+2#

Simplify.

#y=9-18+2#

#y=-7#

The vertex is #(3,-7)#, which is also the minimum point.
graph{y=x^2-6x+2 [-16.02, 16.01, -8.01, 8.01]}