Objectives:1. To find the intercepts of

a graph2. To use symmetry as an

aid to graphing3. To write the equation

of a circle and graph it4. To write equations of

parallel and perpendicular lines

• As a class, use your vast mathematical knowledge to define each of these words without the aid of your textbook.

Graph of an Equation Solution Point

Intercepts Symmetry

Circle Parallel

Perpendicular

The graphgraph of an equation gives a visual representation of all solution points solution points of the equation.

The xx-intercept-intercept of a graph is where it intersects the x-axis.• (aa, 0)

The yy-intercept-intercept of a graph is where it intersects the y-axis.• (0, bb)

6

4

2

-2

-5 5x-intercept

y-intercept

How many x- and y-intercepts can the graph of an equation have? How about the graph of a function?

Given an equation, how do you find the intercepts of its graph?

• To find the x-intercepts, set y = 0 and solve for x.

• To find the y-intercepts, set x = 0 and solve for y.

Find the x- and y-intercepts of y = – x2 – 5x.

A figure has symmetrysymmetry if it can be mapped onto itself by reflection or rotation.

Click me!

How would an understanding of symmetry help you graph an equation?

When it comes to graphs, there are three basic symmetries:

1. xx-axis symmetry-axis symmetry: If (x, y) is on the graph, then (x, -y) is also on the graph.

, ,x y x y

When it comes to graphs, there are three basic symmetries:

2. yy-axis symmetry-axis symmetry: If (x, y) is on the graph, then (-x, y) is also on the graph.

, ,x y x y

When it comes to graphs, there are three basic symmetries:

3. OriginOrigin symmetry symmetry: If (x, y) is on the graph, then (-x, -y) is also on the graph.

, ,x y x y (Rotation of 180)

Using the partial graph pictured, complete the graph so that it has the following symmetries:

1. x-axis symmetry2. y-axis symmetry3. origin symmetry

The set of all coplanar points is a circlecircle if and only if they are equidistant from a given point in the plane.

Find the equation of points (x, y) that are r units from (h, k).

Standard form of the equation of a circle:

2 2 2x h y k r

(h, k) = center pointr = radius

The point (1, -2) lies on the circle whose center is at (-3, -5). Write the standard form of the equation of the circle.

Find the center and radius of the circle, and then sketch the graph.

2 22 3 25x y

Convert the given equation to the following forms:

1.Slope-intercept form2.Standard form

36 5

4y x

Convert the given equation to the following forms:

1.Slope-intercept form2.Point-slope form

3 7 10x y

Two lines are parallel parallel lineslines iff they are coplanar and never intersect.

Two lines are perpendicular lines perpendicular lines iff they intersect to form a right angle.

m || n

Two lines are parallel parallel lineslines iff they have the same slope.

Two lines are perpendicular lines perpendicular lines iff their slopes are negative reciprocals.

Write an equation of the line that passes through the point (-2, 1) and is:

1.Parallel to the line y = -3x + 12.Perpendicular to the line y = -3x + 1

Objectives:1. To find the intercepts of

a graph2. To use symmetry as an

aid to graphing3. To write the equation

of a circle and graph it4. To write equations of

parallel and perpendicular lines