What is the vertex of # y= x^2-2x+8#?

1 Answer
Alan P.
Feb 16, 2016

vertex: #(x,y)=1,7)#

Explanation:

The easiest way to find the vertex is to convert the given equation into "vertex form":
#color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)#
with a vertex at (#color(red)(a),color(blue)(b))#

Given
#color(white)("XXX")y=x^2-2x+8#

Complete the square:
#color(white)("XXX")y=x^2-2x+1 +7#

#color(white)("XXX")y=color(green)(1)(x-color(red)(1))^2+color(blue)(7)#
which is in "vertex-form".

graph{x^2-2x+8 [-3.684, 8.8, 5.06, 11.3]}

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