The Math Page - Completing The Square



Completing the square is the first step to graphing a quadratic equation. Once you have it in transformational form, you're all set.

     y=ax²+bx+c

Let's take a basic quadratic equation:

     y=2x²+4x-6

First, divide every thing by 'a':

     ½y=x²+2x-3

Now, subtract 'c' from both sides:

     ½y+3=x²+2x

Now comes the tricky part. Take b, divide it by 2, then square it and add it to both sides. So:

     ½y+3+1²=x²+2x+1²

1 squared is 1, so:

     ½y+4=x²+2x+1

Now, divide whatever is added to the left side (in this case, 4) by the coefficient of y (in this case, ½), then put it in brackets. So, you get:

     ½(y+8)=x²+2x+1

Now 'FOIL' out the right side, and your final answer becomes:

     ½(y+8)=(x+1)²

Look familiar? It should! It's in transformational form!