What you’ll learn
Graph absolute-value functions.
Key idea
The inner zero locates the vertex horizontally; signed outer coefficient determines opening and arm steepness.
Vertex input and height differ; each ray must have the same signed distance coefficient.
Worked example
Enter the exact value or ordered values in the format requested below.
Full V graph consists of straight rays from V through all L/R marks; x horizontal, y vertical. Read the numerical x-coordinate of the vertex.
Marked coordinates: V=(-3, 4); L=(-4, 1); R=(-2, 1); L=(-5, -2); R=(-1, -2).
- The two straight rays meet at V=(-3,4); output changes -3 per unit distance from the vertex.
- Equation y=-3|x+3|+4 gives the same vertex, direction and linear offset heights; construction V:(-3,4);L:(-4,1);R:(-2,1).
Answer: -3
Quick Check
Relate the graph used in 'Graph absolute-value functions' to an equation, table, transformation, or verbal description.
Full V graph consists of straight rays from V through all L/R marks; x horizontal, y vertical. Connect to an equation using the vertex and signed arm slopes.
Marked coordinates: V=(2, -4); L=(1, -7); R=(3, -7); L=(0, -10); R=(4, -10).