Objectives:
1.
To find the intercepts of a graph
2.
To use symmetry as an aid to graphing
3.
To write the equation of a circle and graph it
4.
To write equations of parallel and perpendicular lines
Assignments:
• P. 22-23: 9-19 odd, 25,
29, 59, 62, 64, 67, 69
• P. 22: 23, 24. Ignore book instructions.
– A) graph x -axis symmetry;
– B) graph y -axis symmetry;
– C) graph origin symmetry
• P. 35: 69, 71
• Homework Worksheet
• Read P. 40-47; A2-A3

Graph of an Equation Solution Point
Intercepts
Circle
Perpendicular
Symmetry
Parallel

You will be able to find the intercepts of a graph

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

The x -intercept of a graph is where it intersects the x -axis.
• ( a , 0)
The y -intercept of a graph is where it intersects the y -axis.
• (0, b )
-5 x-intercept
-2
6
2
4 y-intercept
5

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 To find the y -intercepts
y
x
x
y

Find the x - and y -intercepts of y = – x 2 – 5 x .

You will be able to use symmetry to help you graph an equation.

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

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

When it comes to graphs, there are three basic symmetries:
1.
x -axis symmetry : If
( x , y ) is on the graph, then ( x , − y ) is also on the graph.
   x ,
 y


When it comes to graphs, there are three basic symmetries:
2.
y -axis symmetry : If
( x , y ) is on the graph, then (− x , y ) is also on the graph.
   

When it comes to graphs, there are three basic symmetries:
3. Origin symmetry : If
( x , y ) is on the graph, then (− x , − y ) is also on the graph.
   y

(Rotation of 180

)

Using the partial graph pictured, complete the graph so that it has the following symmetries:
1.
x -axis symmetry
2.
y -axis symmetry
3.
origin symmetry

It’s pretty easy to tell if a graph has a particular symmetry, but what if you only know the equation?
Symmetry Algebraic Test x -axis Plugging in – y for y gives the same equation y -axis Plugging in – x for x gives the same equation origin
Plugging in – y for y and – x for x gives the same equation

Determine which, if any, symmetry the graph of each equation should display.
1.
y = 2 x 2 – 3
2.
y = 1/ x

The set of all coplanar points is a circle 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:
 x
 h
  y
 k

2  r
2
( h , k ) = center point r = 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.

The previous question asked for the equation of a circle given the center and a point on the circle. What other collection of points could a question give you to enable you to write the equation of a circle?

Find the center and radius of the circle, and then sketch the graph.
 x

2
  y

3

2 
25

Convert the given equation to the following forms: y 6
3
4
 x

5

1.
Slope-intercept form
2.
Standard form

Convert the given equation to the following forms:
3 x

7 y

10
1.
Slope-intercept form
2.
Point-slope form

Two lines are parallel lines iff they are coplanar and never intersect.
Two lines are perpendicular lines iff they intersect to form a right angle.
m || n

Two lines are parallel lines iff they have the same slope.
Two lines are 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 = −3 x + 1
2.
Perpendicular to the line y = −3 x + 1

Find the value of k : if the line through the points
(2 k + 1, –4) and (5, 3 – k ) is parallel to the line through the points (–4, –9) and (2, –3).

Objectives:
1.
To find the intercepts of a graph
2.
To use symmetry as an aid to graphing
3.
To write the equation of a circle and graph it
4.
To write equations of parallel and perpendicular lines
Assignments:
• P. 22-23: 9-19 odd, 25,
29, 59, 62, 64, 67, 69
• P. 22: 23, 24. Ignore book instructions.
– A) graph x -axis symmetry;
– B) graph y -axis symmetry;
– C) graph origin symmetry
• P. 35: 69, 71
• Homework Worksheet