1. Intercepts of a Graph
Intercepts are the points at which the graph intersects the x-axis or the y-axis.
Since an intercept intersects the x-axis or the y-axis, then an intercept has zero as either its x-coordinate or its y-coordinate.
y-intercepts
x-intercepts
The point (a, 0) is an x-intercept of the graph of an equation if it is a solution point of the equation.
The point (0, b) is a y-intercept of the graph of an equation if it is a solution point of the equation.
Looks like these intercepts should be pretty easy to find.

2. Examples of Intercepts
Slow down. Let’s take a look at what some intercepts look like first so we know what we’re looking for. y y y y x x x x
No x-intercepts
Three x-intercepts
One x-intercept
No x-intercepts
One y-intercept
One y-intercept
Two y-intercepts
No y-intercepts
Now can we take a look at how to find intercepts if we don’t have a graph to look at?

3. Finding Intercepts of a Graph
Let’s take a look at how we go about finding x-intercepts and y-intercepts.
x-intercepts
y-intercepts
To find the x-intercepts of a graph, let y be zero and solve the equation for x.
To find the y-intercepts of a graph, let x be zero and solve the equation for y.
That sounds pretty easy to me.

4. Example of Finding the Intercepts of a Graph
Find the x-intercepts and the y-intercepts of the graph of
x-intercepts
y-intercepts
Let y be zero and solve the equation for x.
Let x be zero and solve the equation for y.
The y-intercept is
(0, 0)
The x-intercepts are
That was easy
(-2, 0), (0, 0), and (2, 0)

5. More Intercepts of a Graph
Find the x-intercepts and the y-intercepts of the graph of
x-intercepts
y-intercepts
Let y be zero and solve the equation for x.
Let x be zero and solve the equation for y.
The y-intercept is
(0, 0)
Asi de Facil
The x-intercepts are
(-3, 0), (0, 0), and (3, 0)

6. Even More Intercepts of a Graph
Find the x-intercepts and the y-intercepts of the graph of
x-intercepts
y-intercepts
Let y be zero and solve the equation for x.
Let x be zero and solve the equation for y.
There is no
y-intercept
The x-intercepts is
(25, 0)

7. Homework
Page 8:

8. Symmetry of a Graph
There are three different types of symmetry that can be used to help sketch the graph of an equation.
y-axis symmetry
A graph is symmetric with the respect to the y-axis if,
whenever (x, y) is a point on the graph, (-x, y) is also a point on the graph.
That means, that the portion of the graph to the left of the y-axis is a mirror image of the portion of the graph to the right of the y-axis.
x-axis symmetry
A graph is symmetric with the respect to the x-axis if,
whenever (x, y) is a point on the graph, (x, -y) is also a point on the graph.
That means, that the portion of the graph above the x-axis is a mirror image of the portion of the graph below the x-axis.
origin symmetry
A graph is symmetric with the respect to the origin if,
whenever (x, y) is a point on the graph, (-x, -y) is also a point on the graph.
That’s confusing.
That means, that the graph is unchanged by a rotation of 180o about the origin.

9. Examples of Symmetry y-axis symmetry origin symmetry x-axis symmetry
The portion of the graph to the left of the y-axis is a mirror image of the portion to the right.
The portion of the graph above the x-axis is a mirror image of the portion below.
The graph is unchanged by a rotation of 180o about the origin.
Therefore, the graph is symmetric with respect to the y-axis.
Therefore, the graph is symmetric with respect to the x-axis.
Therefore, the graph is symmetric with respect to the origin.

10. Tests for Symmetry I think I can do that. y-axis symmetry
The graph of an equation is symmetric with respect to the y-axis if replacing x by –x yields an equivalent equation.
x-axis symmetry
The graph of an equation is symmetric with respect to the x-axis if replacing y by -y yields an equivalent equation.
origin symmetry
The graph of an equation is symmetric with respect to the origin if replacing x by –x and y by -y yields an equivalent equation.

11. Testing for Symmetry That was easy No No Yes
Test the following equation for y-axis, x-axis, and origin symmetry.
That was easy
origin symmetry
y-axis symmetry
x-axis symmetry
Replace x with –x and
replace y with -y
Replace x with -x
Replace y with -y
They are not equivalent equations, therefore the graph is not symmetric with respect to the y-axis.
They are not equivalent equations, therefore the graph is not symmetric with respect to the x-axis.
They are equivalent equations, therefore the graph is symmetric with respect to the origin. No No
Yes

12. Testing for Symmetry Yes No No
Test the following equation for y-axis, x-axis, and origin symmetry.
origin symmetry
y-axis symmetry
x-axis symmetry
Replace x with –x and
replace y with -y
Replace x with -x
Replace y with -y
They are equivalent equations, therefore the graph is symmetric with respect to the y-axis.
They are not equivalent equations, therefore the graph is not symmetric with respect to the x-axis.
They are not equivalent equations, therefore the graph is not symmetric with respect to the origin.
Yes No No

13. Homework
Page 8: 30 – 38
Even Numbers

14. Points of Intersection
The obvious thing about Points of Intersection is that they are the points where the graphs of two equations intersect.
Did you really think that I didn’t know that?
More importantly, a Point of Intersection of the graphs of two equations is a point that satisfies both equations.
You can find the Points of Intersection of two graphs by setting the two equations equal to each other and solving them simultaneously.

15. Finding Points of Intersection
Find all the points of intersection of the graphs of
I have to push the easy button
and
First solve each equation for y.
That was easy
Set the equations equal to each other and solve for x.
The points of intersection are
(-1, -2)
and
(2, 1)
To find the corresponding y values, plug each x value into one of the equations.

16. Graphing Points of Intersection
Let’s take a look at the graphs of those two equations and see what the points of intersection look like.
That was easy
and
Hey, that’s the same answer that we got before. I guess we could say they are Sam Ting.
(2, 1)
(-1, -2)

17. Points of Intersection Examples
Find the points of intersection of the graphs of the following equations.
Example b
Example 1
and
and
The points of intersection are:
The points of intersection are:
(-1, -2) and (2, 1)
(0, 0), (-1, -1) and (1, 1)

18. Graphs of Intersection Examples
This is just getting easier and easier.
That was easy
and
and
(2, 1)
(1, 1)
(0, 0)
(-1, -1)
(-1, -2)

19. Homework
Page 8 - 9:
63, 64, 65, 66, 68, 70