## 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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