Algebra II Recipe: Absolute Value Functions

A. Characteristics

1. The equation is y = a|x - h| + k.
2. The vertex point is (h, k).
3. The axis of symmetry is x = h.
4. The graph is v-shaped.
5. The graph opens up if a > 0 and down if a < 0.
6. The graph is wider than the "parent" function when |a| > 1.
7. The graph is more narrow than the "parent" function when |a| < 1.

B. Steps to Graph

1. Determine the vertex point and graph it.
2. Draw the axis of symmetry.
3. Choose one x-value on either side of the symmetry line, substitute the value into the equation to get y, then graph the point.
4. Use symmetry to graph the point on the other side of the symmetry line.
5. Connect the three points with a v-shaped graph.

Practice Problems