Vertex and Axis of Symmetry for Absolute Value Functions
Vertex and axis of symmetry for absolute value functions is a Grade 11 Algebra 1 topic from enVision Chapter 5 covering the form f(x) = a|x - h| + k. The vertex is at (h, k) and the axis of symmetry is the vertical line x = h. For the parent f(x) = |x|, vertex is (0,0) and axis is x = 0. For f(x) = 3|x|, the vertex remains (0,0). For f(x) = 2|x - 5| + 3, vertex is (5, 3) and axis is x = 5. The vertex is the turning point of the V-shape — minimum if a > 0, maximum if a < 0.
Key Concepts
For the absolute value function $f(x) = a|x h| + k$, the vertex is at the point $(h, k)$ and the axis of symmetry is the vertical line $x = h$. For the parent function $f(x) = |x|$, the vertex is $(0, 0)$ and the axis of symmetry is $x = 0$.
Common Questions
Where is the vertex of f(x) = a|x - h| + k?
At the point (h, k). The vertex is always where the V-shape changes direction.
What is the axis of symmetry of f(x) = a|x - h| + k?
The vertical line x = h. It passes through the vertex and divides the V-shape into two mirror halves.
What is the vertex and axis of f(x) = |x|?
Vertex is (0, 0) and axis of symmetry is x = 0.
What is the vertex and axis of f(x) = 2|x - 5| + 3?
Vertex is (5, 3) and axis of symmetry is x = 5.
Does the coefficient a affect the vertex location?
No. The coefficient a stretches or reflects the graph but does not change the vertex location (h, k).
When is the vertex a minimum vs a maximum?
When a > 0, the V opens upward and the vertex is a minimum. When a < 0, the V opens downward and the vertex is a maximum.