Interactive resource
Shifts & Stretches: a, b, h, k on a Graph
Functions. Using y=x², interactively stretch and shift to master y = a f(b(x−h)) + k.
Overview
Transformations follow a pattern: stretch, then shift. Compare with the gray reference curve to see each parameter’s job.
Explanation
Form y = a f(b(x−h)) + k:
|a| stretches vertically (a<0 flips); |b| stretches horizontally; h shifts horizontally; k shifts vertically.
A common graphing order is stretch then shift.
How to use
- Open the transformations scene.
- Tune a, b, h, and k separately.
- Compare with gray y = x².
- Summarize each parameter’s geometric effect.
Order tip
Change a and b first (stretches), then h and k (shifts).
Knowledge points
FAQ
Does b > 1 widen or compress horizontally?
It compresses in x (narrower graph); |b| < 1 stretches wider.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.