Graphing Architect

Graphing Absolute Value Inequalities

Master vertex placement, line style (dashed vs. solid), direction of opening, test point evaluation, and shaded region identification for absolute value inequalities.

Key Concepts Covered:

  • Vertex $(h, k)$: For $y \le a|x - h| + k$, the vertex (turn point) is located at $(h, k)$.
  • Boundary Lines: Strict inequalities ($<, >$) use dashed lines; inclusive inequalities ($\le, \ge$) use solid lines.
  • Shading Directions: Greater than ($>, \ge$) shades above/inside an upward V; less than ($<, \le$) shades below/outside an upward V.
  • Orientation & Stretch: Positive $a$ opens UP, negative $a$ opens DOWN, and $|a|$ dictates branch slope.