Section 1.2: Graphs of Equations;

Circles

Determine if the following point is on the graph of the equation.

2x – y = 6; (2, 3)Step 1: Plug the given points into the given equation. 2(2) – (3) = 6Step 2: Simplify.4 – 3 = 6 1 = 6Step 3: If the answer is true, the point is on the graph. If the answer is false, then the point is not on the graph.Since 1 =6 is false, the point (2, 3) is not on the graph of this equation.

Intercepts

The x-intercept is where the graph crosses the x-axis.What’s special about the coordinates of this point?The ordinate (y value) is zero.

The y-intercept is where the graph crosses the y-axis.What’s special about the coordinates of this point?The abscissa (x value) is zero.

An intercept is the point at which the graph crosses or touches one of the coordinate axes.

Examples: Find the intercepts1. x2 + y - 9 = 0 2. y =

3

2 16

x

x

Symmetriesx – axis symmetry: for every point (x, y) on a

graph, the point (x, -y) is also on the graph

y – axis symmetry: for every point (x, y) on a graph, the point (-x, y) is also on the graph

Origin symmetry: for every point (x, y) on a graph, the point (-x, -y) is also on the graph

Examples: Plot each point, then plot the point that is symmetric to it with respect to the a.) x – axis, b.) y – axis, and c.) origin.1. (-2, 1)

2. (4, -3)

To Test for Symmetryx-axis symmetry: Replace y with –y in the

equation

y-axis symmetry: Replace x with –x in the equation

Origin symmetry: Replace x with –x and replace y with –y in the equation

In each case, if you get the exact same equation back, you have that type of symmetry.

Examples: Test for symmetry1. x2 + y - 9 = 0 2. y =

3

2 16

x

x

Homework: p. 18-19 #2-44 even