What quantity did you change?
Labs / Mathematics
Polynomial Playground
Every polynomial is a story about where it crosses zero. Drag the round root markers along the x-axis, add or remove roots, and stack them up into double and triple roots — the curve, its turning points, and both algebraic forms redraw the instant you move.
Labs / Mathematics / Polynomial Playground
Polynomial Playground
Every polynomial is a story about where it crosses zero. Drag the round root markers along the x-axis, add or remove roots, and stack them up into double and triple roots — the curve, its turning points, and both algebraic forms redraw the instant you move.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
f(x)= 0deg 3tails ↙ ↗
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Slide two roots until they land on the same spot. Why does the curve stop crossing the axis there and just kiss it instead?
- Bump a root's multiplicity to ×3. What happens to the curve as it passes through — does it flatten out?
- Drag the leading coefficient a from positive to negative. Which way do the two tails flip, and why do both ends move together?
- A degree-4 polynomial — how many turning points can it have at most, and how few? Can you make it have exactly one?
- With an odd degree, can you ever get both tails pointing the same way? What about with an even degree?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.