Find the vertex of the graph of the equation x - y^2 + 8y = 13.
We can rewrite the equation as [y^2 - 8y + (x - 13) = 0.]Completing the square, we get [(y - 4)^2 - 16 + (x - 13) = 0.]Then [(y - 4)^2 = x - 7,]so y=4±x−7.
The vertex is the point where the parabola changes concavity, so it is the point where the discriminant of the quadratic is 0. This occurs when x−7=0, so the vertex is (7,4).