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Lesson Transcript
Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

The x-axis and y-axis of a graph divide the graph into four quadrants. Learn about the four quadrants, how they are different from each other, and how they are useful in understanding mathematical patterns.

A 2-dimensional graph, Cartesian plane, includes negative and positive values of both x and y. This graph is divided into four quadrants, or sections, based on those values. The first quadrant is the upper right-hand corner of the graph, the section where both x and y are positive. The second quadrant, in the upper left-hand corner, includes negative values of x and positive values of y. The third quadrant, the lower left-hand corner, includes negative values of both x and y. Finally, the fourth quadrant, the lower right-hand corner, includes positive values of x and negative values of y.

In some ways, the quadrants across from each other diagonally are similar to each other. First, let's look at the first and third quadrants, using an example.

Imagine that you ask your family and friends how they feel about Facebook. They give you positive numbers if they like it and negative values if they dislike it. For example, your best friend might love Facebook. She gives it a 4. Your mother thinks Facebook is a complete waste of time. She gives it a -6. Your grandmother, on the other hand, doesn't even know what Facebook is. She is completely neutral and gives it a 0.

You do the same for how your family and friends feel about texting. They rate texting with a positive number if they like it and a negative number if they hate it. For example, your mother gives texting a 4 because she finds it a useful way to keep track of you.

Since you have two numbers for each person, you might graph how they feel on a Cartesian plane. How they feel about Facebook is x. How they feel about texting is y. For example, your mother's ratings are (-6,4). On a graph, it looks like this:

When you start plotting everyone's responses, you find that some of them are consistent. They either love both Facebook and texting or they hate both.

Quadrant one is the 'love, love' section of the graph. In the graph, the pink and yellow faces are in quadrant one. These two individuals love both Facebook and texting. For both of these people, both ratings were positive numbers.

Quadrant three is the 'hate, hate' section of the graph. The blue and purple faces hate both Facebook and texting. For both of these people, both ratings were negative numbers.

Quadrants one and three include all the points whose coordinates have the same sign - both positive or both negative.

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