1. 1.3 Symmetry; Graphing Key Equations; Circles

2. Symmetry
A graph is said to be symmetric with respect to the x-axis if for every point (x,y) on the graph, the point (x,-y) is on the graph.

3. A graph is said to be symmetric with respect to the y-axis if for every point (x,y) on the graph, the point (-x,y) is on the graph.

4. A graph is said to be symmetric with respect to the origin if for every point (x,y) on the graph, the point (-x,-y) is on the graph.

5. Tests for Symmetry
x-axis Replace y by -y in the equation. If an equivalent equation results, the graph is symmetric with respect to the x-axis.
y-axis Replace x by -x in the equation. If an equivalent equation results, the graph is symmetric with respect to the y-axis.
origin Replace x by -x and y by -y in the equation. If an equivalent equation results, the graph is symmetric with respect to the origin.

6. Not symmetric with respect to the x-axis.

7. Symmetric with respect to the y-axis.

8. Not symmetric with respect to the origin.

9. A circle is a set of points in the xy-plane that are a fixed
distance r from a fixed point (h, k).
The fixed distance is called the radius, and the fixed
point (h, k) is called the center of the circle. y
(x, y) r
(h, k) x

10. The standard form of an equation of a circle with radius r and center (h, k) is

11. Graph ( ) x y + - = 1 3 16 2

12. y
(-1, 7)
(3,3)
(-5, 3)
(-1,3) x
(-1, -1)

13. The general form of the equation of a circle

14. Find the center and the radius of
First group terms:

15. Add appropriate terms to complete the squares for x and for y.