Find the vertex of the graph of the equation x - y^2 + 8y = 13 - 6y + y^2.
Rearrange as
x = 2y^2 -14y + 13
This is a parabola that opens to the right
The y coordinate of the vertex = -(-14) / [2*2] = 14/4 = 7/2
And the x coordinate is 2 (7/2)^2 - 14 (7/2) + 13 = 49/2 - 49 + 13 = -11.5
Vertex = (-11.5 , 7/2) = (-11.5 , 3.5)