What is the axis of symmetry and vertex for the graph #3x^2 -8x +7#?

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Answer 1 · 2017-03-17T15:57:16

Vertex#->(x,y)=(4/3,5/3)#
Axis of symmetry = #x_("vertex")=4/3#

#color(brown)("The axis of symmetry and "x_("vertex")" both have the same x-value.")#

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

A sort of cheat way (not really).

Write as: #y=3(x^2-8/3x)+7#

#x_("vertex")=(-1/2)xx(-8/3) = +4/3#

Substitute #x=4/3# giving

#y=3x^2-8x+7" "->" "y=3(4/3)^2-8(4/3)+7#

#y_("vertex")= 5/3#

Vertex#->(x,y)=(4/3,5/3)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determining the axis of symmetry")#

Axis of symmetry = #x_("vertex")=4/3#

Tony B