1. Graphs of
Equations
© 2002 by Shawna Haider

2. Quadrant II where x is negative and y is positive
You should be familiar with the rectangular coordinate system and point plotting from an earlier algebra course. Let's just run through the basics.
y axis
Quadrant II where x is negative and y is positive
Quadrant I where both x and y are positive
x axis
origin
Quadrant IV where x is positive and y is negative
Quadrant III where both x and y are negative

3. Let's plot the point (-3,-5)8 7 6 5 4 3 2 1 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 -2 -3 -4 -5 -6 -7
Let's plot the point (0,7)
Let's plot the point (-3,-5)

4. This means then that y = -4 and the y intercept is (0,-4)
In this section we are going to use the point plotting method to graph equations. Look at the following equation.
y = x
Recall how to find x and y intercepts. The x intercept is where the y value is zero.
The y intercept is where the x value is zero.
0 = x
Solving for x
y =
Since x2 is 4, x could be 2 or –2 so the x intercepts are (2,0) and (-2,0)
This means then that y = -4 and the y intercept is (0,-4)

5. Let's put these values in a table: 1 3
(-3)
(-1)
- 3 5 5 x y
- 3
- 3 5 5
Choose some more x values to plug into the equation to find corresponding y values
Now let's plot what we have so far: 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8
Now let's plot these values and join the points in a smooth curve
The shape of this graph is called a parabola. We'll learn more about them later in the course.

6. Helps to Graph an Equation
Isolate (get alone) one of the variables if possible (usually y)
Find the x and y intercepts by plugging 0 in for y and then for x like we did on the previous screen (sometimes easier to do this before you isolate a variable)
Make a table of values choosing some x values and find corresponding y values (if you isolated x then choose some y values and find corresponding x values)
Plot these points and join in a smooth curve or line

7. Let's try graphing one more…
could be 1 or -1
Let's try graphing one more…
Get the y alone x y -1 1 1 2 2
Choose some more x values to plug into the equation to find corresponding y values
Find the x & y intercepts & plot them: 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8
Now let's plot these values and join the points in a smooth curve (or line)
The shape of an absolute value graph is "v-shaped".