How to Graph Absolute Value Equations



y = |x|

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Where is the vertex?

What direction does it open?

What is the slope?

y = - |x|

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Where is the vertex?

What direction does it open?

What is the slope?

y = |x - 2|

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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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