SOLUTION: Sketch a graph of the equation. x=3y^2-18y+23 Please explain and help me! I know you have to complete the square. I tried, but then some parts made me confused. Thank you for y

Algebra ->  Test  -> Lessons -> SOLUTION: Sketch a graph of the equation. x=3y^2-18y+23 Please explain and help me! I know you have to complete the square. I tried, but then some parts made me confused. Thank you for y      Log On


   

Question 710011: Sketch a graph of the equation.
x=3y^2-18y+23
Please explain and help me! I know you have to complete the square. I tried, but then some parts made me confused. Thank you for your help!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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 %286%2F2%29%5E2, or 9.
Add the 9 inside the parentheses and you would need to subtract something outside the parentheses.
x=3%28y%5E2-6y%2B9%29%2B23+-+3%2A9
Do you know why we add the 9 inside the parentheses but subtract 3*9 outside of the parentheses?

But, to continue,
x=3%28y%5E2-6y%2B9%29%2B23-27
x=3%28y-3%29%5E2-4
This would be moved upward by 3 units and moved rightward by 4 units. The vertex is at point (3,-4)