y=ax^2+bx+c=a(x^2+b/ax+c/a)=a[x^2+b/ax+(b/2a)^2-(b/2a)^2+c/a]=a[(x+b/2a)^2-b^2/4a^2+c/a]=a[(x+b/2a)^2-b^2/4a^2+4ac/4a^2]=a[(x+b/2a)^2+(4ac-b^2)/4a^2]=a(x+b/2a)^2+(4ac-b^2)/4a
y=ax²+bx+c. y=a(x-b/2a)²+(4ac-b²)/4a