Mathematics — first biennium · Lesson
The graph of y=a|x−h|+k is V-shaped. The point (h,k) is the vertex and the sign of a determines the opening direction.
Prerequisites: Tables, formulas and graphs
Goal: Read vertex, symmetry and opening direction of a translated absolute-value function.
In this lesson: Read vertex, symmetry and opening direction of a translated absolute-value function.
New concept: The absolute value |u| is the distance of u from zero, so it is never negative. In y=a|x−h|+k, (h,k) is the vertex of the V; the sign of a determines whether the V opens upward or downward.
How to proceed: Inside the absolute value, the sign is read in reverse: |x−h| puts the vertex at x=h.
You can already assume: Tables, formulas and graphs.
Vary a, h and k to observe how the V's opening, direction and vertex position change.
With a = 0 the curve loses this family's characteristic shape; also try a non-zero value.
The graph makes the vertex, symmetry and opening direction of the absolute-value function visible.
Completed exercises: 0/5 · Correct on first attempt: 0
Inside the absolute value, the sign is read in reverse: |x−h| puts the vertex at x=h.
Data / situation: y=|x+1|+3
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.