Find the vertex of the graph of the equation $x - y^2 + 8y = 13$.
Rearrange as
x = y^2 - 8y + 13 complete the square on y
x = y^2 - 8y + 16 + 13 - 16
x = ( y - 4)^2 - 3
(x + 3) = (y - 4)^2
The vertex is ( -3, 4)
Here's the graph : https://www.desmos.com/calculator/tksqqrj5dc
Completing the square, we get x = (y - 8)^2 - 51, so the vertex is (8,-51).