y=ax^2+bx+c
= a(x^2+bx/a+c/a)
= a(x^2+bx/a+( b/2a)^2-( b/2a)^2+c/a)
= a(x^2+bx/a+( b/2a)^2)+ (4ac-b^2)/4a
=a(x+b/2a)^2+ (4ac-b^2)/4a
y=ax^2+bx+c
= a(x^2+bx/a+c/a)
= a(x^2+bx/a+( b/2a)^2-( b/2a)^2+c/a)
= a(x^2+bx/a+( b/2a)^2)+ (4ac-b^2)/4a
=a(x+b/2a)^2+ (4ac-b^2)/4a