Calculator Inputs
Example Data Table
y = 2|x - 1| - 3
| X | Y |
|---|---|
| -2 | 3 |
| -1 | 1 |
| 0 | -1 |
| 1 | -3 |
| 2 | -1 |
| 3 | 1 |
| 4 | 3 |
Formula Used
The standard V-shaped absolute value graph uses this formula:
y = a|x - h| + k
- a controls stretch, compression, and reflection.
- h moves the vertex left or right.
- k moves the graph up or down.
Vertex: (h, k)
Axis of symmetry: x = h
Piecewise form:
For x ≥ h, y = a(x - h) + k
For x < h, y = -a(x - h) + k
If a > 0, the graph opens upward.
If a < 0, it opens downward.
How to Use This Calculator
- Enter the values for a, h, and k.
- Set the plotting range using start x, end x, and step.
- Add any x-value you want highlighted on the graph.
- Press the calculate button to generate the graph and table.
- Review the vertex, slopes, intercepts, axis, and range.
- Download the generated points as CSV or PDF.
Frequently Asked Questions
1. What makes the graph V-shaped?
The absolute value symbol creates two straight branches meeting at one vertex. One branch rises left of the vertex. The other rises right of the vertex.
2. What does the value of a change?
It changes steepness and direction. Larger absolute values make the graph narrower. Smaller absolute values make it wider. Negative values reflect it downward.
3. What does h represent?
The value h shifts the graph horizontally. Positive h moves the vertex right. Negative h moves it left.
4. What does k represent?
The value k shifts the graph vertically. Positive k moves the graph upward. Negative k moves it downward.
5. How do I find the vertex quickly?
Read it directly from the equation y = a|x - h| + k. The vertex is always at the point (h, k).
6. Why can there be zero, one, or two x-intercepts?
That depends on where the graph sits relative to the x-axis. The vertex and opening direction decide how many times the graph touches or crosses zero.
7. What range does an absolute value graph have?
If the graph opens upward, the range starts at the vertex y-value and goes higher. If it opens downward, the range ends at the vertex y-value.
8. Why use the generated table?
The table helps verify plotted points, check homework, and compare changes after adjusting a, h, or k.