Learning Resources

Focus H: Interpreting Equations of Circles

When given the first two terms of a quadratic trinomial and you wish to find the value required to make it a perfect square trinomial ask yourself "what number must be added to create a perfect square trinomial?"  In other words, if you are given , what should be added to this to make it a perfect square trinomial.

Start with a = 1 . recall from earlier work to complete the square for this expression take half the coefficient of x and add it to the expression. To view this procedure step through the following window:

If the coefficient of x²  is not 1, then it must be removed as a common factor, before completing the square. View it below:

The skill to do this is essential in converting the standard form of the circle to the general form . Practice it.