Completing the Square

Question

When completing the square on the quadratic equation below, how is c calculated?

y= x^2+bx+c

Possible answers:

c=(a/2)^2

c=b^2

c=(a/4)^2

c=(b/2)^2

Answer 1

In order to solve this we need the coefficient of the x² term to be 1. In this problem that is already the case, but if it isn't, you will have to divide both sides of the equation by whatever the equation is (e.g. if the equation was y=2x²+4, the new equation would be y/2=x²+2).

The next step is to take the coefficient of the x term (b in this case), divide it by 2, and square it. This will be the c term to complete this equation.

So, the answer is (b/2)²