# What is the vertex of  y^2-2y-2x+5=0?

$\left(2 , 1\right)$

#### Explanation:

Given equation:

${y}^{2} - 2 y - 2 x + 5 = 0$

${y}^{2} - 2 y + 1 - 1 - 2 x + 5 = 0$

${\left(y - 1\right)}^{2} - 2 x + 4 = 0$

${\left(y - 1\right)}^{2} = 2 x - 4$

${\left(y - 1\right)}^{2} = 2 \left(x - 2\right)$

Above is the equation of horizontal parabola: ${Y}^{2} = 4 a X$ which has

Vertex: $\left(X = 0 , Y = 0\right) \setminus \equiv \left(x - 2 = 0 , y - 1 = 0\right) \setminus \equiv \left(2 , 1\right)$