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What is the axis of symmetry and vertex for the graph #y = x^2 - 4x + 1#?

Question

What is the axis of symmetry and vertex for the graph #y = x^2 - 4x + 1#?
What is the axis of symmetry and vertex for the graph #y = x^2 - 4x + 1#?

Answers

#x = 2# is the line of symmetry.

#(2,-3)# is the vertex.

Explanation:

Find the axis of symmetry first using #x = (-b)/(2a)#

#y = x^2-4x+1#

#x= (-(-4))/(2(a)) = 4/2 = 2#

The vertex lies on the line of symmetry, so we know #x = 2#
Use the value of #x# to find #y#

#y = (2)^2 -4(2) +1#

#y = 4-8+1 = -3#

The vertex is at #(2,-3)#

You can also use the method of completing the square to write the equation in vertex form: #y= a(x+b)^2 +c#

#y = x^2 -4x color(blue)(+4-4) +1" "[color(blue)(+(b/2)^2-(b/2)^2)]#

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

The vertex is at #(-b,c) = (2,-3)#


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