What is the axis of symmetry and vertex for the graph #y= 3x^2 - 4x + 6#?

1 Answer
Oct 13, 2016

Axis of symmetry: #x=2/3#
Vertex: #(2/3, 4 2/3)#

Explanation:

Given
#color(white)("XXX")y=3x^2-4x+6#
We will convert this equation into "vertex form":
#color(white)("XXX")y=color(green)m(x-color(red)a)^2+color(blue)b# with vertex at #(color(red)a,color(blue)b)#

Extracting #color(green)(m)#
#color(white)("XXX")y=color(green)3(x^2-4/3x)+6#

Completing the square
#color(white)("XXX")y=color(green)3(x^2-4/3xcolor(magenta)+color(red)((2/3))^2)+6color(magenta)-color(green)3 * (color(red)(2/3)^2)#

#color(white)("XXX")y=color(green)3(x-color(red)(2/3))^2+color(blue)(4 2/3)#

So the vertex is at #(color(red)(2/3),color(blue)(4 2/3))#

The axis of symmetry is a vertical line of the form #x=color(red)(a)# running through the vertex.

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