1.4 Absolute value functions

Ideas in this lesson

Vertex and range

For a|x − h| + k, the vertex is (h,k). The sign of a determines the opening.

Solve an absolute value equation

After isolating the absolute value, use both the positive and negative cases.

Absolute value inequalities

For a positive bound, less than means between; greater than means outside.

Zero and negative absolute-value bounds

An absolute value is nonnegative; isolate it before deciding the number of solutions.

Absolute values on both sides

Equal distances from two different points occur at their midpoint.

Zero-bound absolute-value inequalities

Distinguish strict, inclusive and impossible bounds after isolating absolute value.