# What is the axis of symmetry and vertex for the graph #y = x^2 -4x + 8#?

##### 1 Answer

Feb 15, 2017

Axis of symmetry:

#### Explanation:

To find out the axis of symmetry and vertex, the equation must be put in standard form (vertex form):

where

Use completing of the square:

- Combine the x-terms:
#y=(x^2-4x)+8 # - half the x-term coeficient
#: 1/2 (-4) = -2 # and put it inside the squared factor#(x-2)^2# - Subtract the added term:
#(- 2)^2 =4 #

#y= (x-2)^2+8-4#

Note: since#(x-2)^2 = (x-2)(x-2) = x^2-4x+4# the added term is#4# . - Simplify:
#y = (x-2)^2+4#

From the graph you can also see the axis & vertex:

graph{x^2-4x+8 [-10.17, 9.83, -0.76, 9.24]}