Hi,

 y^2-2x+6y+5=0

 2x-5 =  y^2 + 6y

 2x-5 + 9 =  y^2 + 6y + 9   ||Adding 9 to both sides to complete the Square on the right side 

2x -5 + 9 =  (y+3)^2

 2x + 4 = (y+3)^2          ||Multiplying thru by 1/2

     Parbola, V(-2,-3), line of symmetry y = -3

 vertex form of a Parabola opening right(a>0) or left(a<0), 

 where(h,k) is the vertex and  y = k  is the Line of Symmetry

 

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