How to Graph Absolute Value Equations
y = |x|
[pic]
Where is the vertex?
What direction does it open?
What is the slope?
y = - |x|
[pic]
Where is the vertex?
What direction does it open?
What is the slope?
y = |x - 2|
[pic]
Where is the vertex?
What direction does it open?
What is the slope?
y = |x| + 1
[pic]
Where is the vertex?
What direction does it open?
What is the slope?
Sample Problem: y = -5|x + 7| - 2
Step 1: Find the x-coordinate of the vertex by setting x + 7 equal to zero.
x + 7 = 0
-7 -7
x = -7
Step 2: Find the y-coordinate of the vertex by substituting in your x value into the equation and solving.
y = -5|-7 + 7| - 2
y = -5(0) – 2
y = - 2
Therefore, the vertex is (-7, -2)
Step 3: Pick an x value to the right and left of the vertex and find two more points to plot.
x = -9 and x = -5
y = -5|-9 + 7| - 2 y = -5|-5 + 7| - 2
y = -5|-2| - 2 y = -5|2| - 2
y = -5(2) – 2 y = -5(2) – 2
y = -10 – 2 y = -10 – 2
y = -12 y = -12
(-9, -12) and (-5, -12)
Step 4: Graph the three points.
Try it on your own:
y = 2|x – 2| + 8
Step 1: Find the x-coordinate of the vertex by setting the absolute value portion of the equation equal to zero.
Step 2: Find the y-coordinate of the vertex by substituting in your x value into the equation and solving.
The vertex of this graph is ( , )
Step 3: Pick an x value to the right and left of the vertex and find two more points to plot.
Step 4: Graph the three points.
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