What is the vertex of # y= 3x^2-18x+7#?

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Answer 1 · 2016-03-30T14:59:52

Vertex#" "->" "(x,y)" "->" "(3,-20)#

There are several way of doing this. I am going to show you a 'sort of' cheat way. In fact it is part of the process for 'completing the square'.

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Given:#" "y=3x^2-18x+7#

#color(blue)("Determining "x_("vertex"))#

Write as:#" "y=3(x^2-18/3x)+7#

Apply #(-1/2)xx(-18/3) = +9/3=3#

#" "color(blue)(x_("vertex")=3)#

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Compare this to the graph
Tony B
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#color(blue)("Determine "y_("vertex"))#

Substitute #x=3# into the original equation

#color(brown)(y=3x^2-18x+7)" "->" "y=3(3)^2-18(3)+7#

#y=27-54+7 =-20#

#" "color(blue)(y_("vertex") = -20)#