Objective:

To graph absolute value equations.

Notes:

The graph of an absolute value equation is not a straight line, it forms a V.

Steps to graph absolute value equations:

  1. Solve the equation for y (get y by itself) (if needed).
  2. Find  the vertex:
    • The x-coordinate of the vertex is the number that makes the absolute value part of the equation equal to zero.
    • The y-coordinate of the vertex is the constant that is not between the absolute value bars.
  3. Make a table of values.
    • Use the x-coordinate of the vertex as your middle x-value.
  4. Plot the points from your table.

Examples:

Sketch the Graph:

Ex 1
  1. There is no need to solve for y (it is already by itself).
  2. The absolute value part of the equation is |x - 3|.
    • Positive 3 would make this equal to 0.
    • Therefore the x-coordinate of the vertex is 3.
    • The y-coordinate of the vertex is 5.
  3. Make a table with x = 3 in the middle. Compute the values needed to complete the table.
    • Notice that I chose values of x that would ensure that the absolute value part of the equation is a multiple of the denominator of the coefficient of the absolute value part.
    • Using values such as these lets me avoid fractional answers.
  4. Plot the points listed in the table.
  5. Use a straight edge to connect your points
  6. Draw arrows and label the graph
Ex 1 Ex 1

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This page was last updated on 08/09/13.