Question 841635
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Hi,
x = 2/3y^2 - 4y + 8 
 x - 8 = 2/3y^2 - 4y 
 x - 8 = 2/3(y^2 - 6y)  Completing Square
 x-8 = {{{(2/3)(y-3)^2 - highlight((2/3)*9)}}}
x-8 = {{{(2/3)(y-3)^2 - 6}}}
x-8 + 6 = {{{(2/3)(y-3)^2 }}}
 x-2 = {{{(2/3)(y-3)^2 }}}
x = {{{(2/3)(y-3)^2 + 2}}}   V(2,3) axis is horizontal line y = 3
domain  x &#8805; 2 Parabola opening right.  (Sketch it)
range: All real numbers

the vertex form of a Parabola opening right(a>0) or {{{x=a(y-k)^2 +h}}}
 where(h,k) is the vertex and  y = k  is the Line of Symmetry