1. What is the center and radius of the circle described by this equation? (x-3) 2 + (y-5) 2 =36

2. Now what about this equation? x 2 + 10x + 3 + y 2 + 14y + 50 = -5

3. Completing the Square

4. x x 3 3

5. x x What is the area of this whole square (blue and orange together)? 3 3

6. x x What is the area of each quadrilateral? 3 3

7. x x 3 3 3x x2x2 3 2 =9

8. x x 5 5 Complete the square

9. x x 7 7

10. Incomplete squares, algebraically: = x 2 + 5x + 5x = x 2 + 10x = x 2 + 7x + 7x = x 2 + 14x

11. So…how would you complete the square without the picture? What if you only had the expressions? x 2 + 10x x 2 + 14x + 25 + 49

12. Take half of the coefficient for x, square it, and add to expression. x 2 + 10x  ½ *10 = 5  5 2 = 25  x 2 + 10x + 25 = (x+5) 2

13. Now what about this equation? x 2 + 10x + 3 + y 2 + 14y + 50 = -5