Math 2300 Section 005 – Calculus II – Fall 2010
Completing the Square Examples – September 2, 2010

Put the quadratic in vertex form. Explain the transformations required to translate into , allowing the graph of to be given.
Solution:
Starting with , we first shift one unit right and obtain , then shift four units up and obtain .

Find the center and radius of the circle
Solution: By completing the square on each variable, we have (notice that this time we are adding the required constants on both sides of the equation, instead of adding and subtracting on the same side)
The center is thus and the radius is .