Name: ______________________
Date:________
These are notes on graphing absolute value equations.
The graph of an absolute value equation will always look like a “V” shape or an upside
down “V” shape.
𝑦=|𝑥|
 This will be a right-side up “V” shape; vertex at (0,0)
𝑦 = −| 𝑥 |  This will be an upside down up “V” shape; vertex at (0, 0)
y=|x|
right-side up “V” shape.
y=−|x|
upside down “V” shape.
Name: ______________________
Date:________
Instructions for graphing absolute value equations:
Find the vertex of the absolute value equation by doing the following:
Step 1  Set the inside of the absolute value equation to zero, solve for the missing
variable; which is x.
Step 2  Plug in the x-value that was solved for and then solve for y.
Example #1:
𝑦 = |𝑥 +3|−1
(Original problem)
Step 1: (set the term inside absolute value equal to 0; then, solve for x)
x + 3 = 0 (this is the term inside the absolute value)
x = −3
Step 2: (plug in your answer for x, and then solve for y)
y = | −3 + 3| − 1
y = | 0 | − 1 = −1
vertex is at (−3, −1)
step 3:
Create a T-chart by picking at least two values to the left of the x value of the vertex and
at least two values to the right of the x-value of the vertex.
x
-3
-4
-5
-2
-1
y
−1





Vertex point of absolute value equation
One point to the left of the x value
Second point to the left of the x value
One point to the right of the x-value
Second point to the right of the x-value
Step 4: Now plug in the x-values and solve for y.
Use your original equation:
𝑦 = |𝑥 +3|−1
x
-3
-4
-5
-2
-1
y
−1
0
1
0
1
example for x = −4
y = | −4 + 3| − 1 = 0
Step 5: Plot the points and draw the “V” shape. Use your ruler to graph the v-shape. If
your graph does not look like a “V” shape, then you have made mistakes with your
calculations