Standard and Graphing Form

y = ax^2 + bx + c     complete the square

y - c = ax^2 + bx

y - c  = a(x^2 + (b/a)x )

y - c + a(b^2/[ 4a^2])  = a(x^2 + (b/a)x + (b^2/[4a^2] )

y - c + a(b^2 / [ 4a^2]) = a( x + [b/(2a)] ) ^2

y - c + a(b^2 / [ 4a^2]) = a( x - [ -b/(2a) ] ) ^2

y = a( x - [ -b/(2a) ] ) ^2  - a(b^2 /[ 4a^2]) + c    

y= a(x - [ -b/(2a)])^2 -  b^2/(4a) + c                                     (1)

Remember that [-b/(2a)]  is the x coordinate of the vertex  = h

And substituting this into y =ax^2 + bx + c  .....we can find the y coordinate of the vertex = k, thusly :

y = a[-b/(2a)]^2 + b[-b/(2a)] + c   = k

y = b^2/ [4a] - [2b^2/ (4a)] + c  = k

y =  -  b^2/ (4a) + c  = k

And substituting  -b/(2a)  = h     and  -b^2/(4a) + c  = k  into (1), we have

y =  a (x - h)^2  + k

Thanks! This also helped: https://www.khanacademy.org/math/algebra/quadratics/features-of-quadratic-functions/v/ex3-completing-the-square