How do you complete a square

If you are given the equation y = x²+4x+1 First you determine what is in the squareMake sure your x² term has no coefficientFind half the coefficient of the x termThat is your bracket term in this case - (x+2)²Then expand this bracket and determine what the numerical component isAdd or take away to get original number in this case 2² = 4. 4-3=1Therefore y = (x+2)²-3This can be used to find the minimum of the quadraticBeing (-2,-3)