The V-Graph Lab
Explore the graph of y = a|x − h| + k with sliders: move the vertex, flip the V, and watch x-intercepts appear and vanish.
1 The V-Graph Lab
Drag the sliders to explore y = a|x − h| + k. Watch the vertex (h, k) move, the V open up or flip, and the x-intercepts appear and disappear.
Vertex (0, 0) · opens upward
2 What to notice
Three experiments that build the whole picture.
1. The vertex is (h, k) — always
Set a = 1, h = 3, k = −2. The corner sits at (3, −2): h slides it left-right, k slides it up-down.
2. Negative a flips the V
Drag a below 0. The V opens downward — and a downward V with vertex below the x-axis has no x-intercepts, just like |x| = −2 has no solution.
3. |a| controls steepness
a = 3 is a narrow steep V; a = 0.5 is wide and shallow. The arms always have slopes +a and −a.