# How Do You Find The Vertex Of The Parabola Y 2x 2 8x 7

A slight variant on method

##color(blue)(“Vertex” ->(x,y)->(2,-1)##

Given:##” “2x^2-8x+7##

Write as:##” ” 2(x^2-color(red)(8/2)x)+7##

Consider the ##color(red)(-8/2)” from “-8/2x##

##color(blue)(x_(“vertex”)=(-1/2)xx(color(red)(-8/2)) = +8/4 = 2)##

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Substitute ##x=color(magenta)(2)## in the original equation to find ##y_(“vertex”)##

##y=2x^2-8x+7″ “->” “y_(“vertex”)=2(color(magenta)(2))^2-8(color(magenta)(2))+7##

##color(blue)(y_(“vertex”)= 8-16+7=-1)##

‘~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~##color(blue)(“Vertex” ->(x,y)->(2,-1)##

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