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:
- Solve the equation for y (get y by itself) (if needed).
- 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.
- Make a table of values.
- Use the x-coordinate of the vertex as your middle x-value.
- Plot the points from your table.
Examples:
Sketch the Graph:
- There is no need to solve for y (it is already by itself).
- 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.
- 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.
- Plot the points listed in the table.
- Use a straight edge to connect your points
- Draw arrows and label the graph
