1.3 Symmetry; Graphing Key Equations; Circles

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.

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.

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.

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.

Not symmetric with respect to the x-axis.

Symmetric with respect to the y-axis.

Not symmetric with respect to the origin.

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

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

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

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

The general form of the equation of a circle

Find the center and the radius of First group terms:

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