Question 710011
That would be a parabola opening to the right and vertex to the left.  You would want to complete the square for the y terms.  Start by factoring to reverse-distribute the 3 leading coefficient.


x=3y^2-18y+23
x= 3(y^2-6y ________)+23, and you want to know what term to add and subtract.


The missing square you want is {{{(6/2)^2}}}, or 9.  

Add the 9 inside the parentheses and you would need to subtract something outside the parentheses.

{{{x=3(y^2-6y+9)+23 - 3*9}}}

Do you know why we add the 9 inside the parentheses but subtract 3*9 outside of the parentheses?  


But, to continue,
{{{x=3(y^2-6y+9)+23-27}}}
{{{x=3(y-3)^2-4}}}
This would be moved upward by 3 units and moved rightward by 4 units.  The vertex is at point (3,-4)