Polynomial Roots Explorer
Drag the root points on the x-axis and watch the polynomial reshape. Change the leading coefficient to flip or stretch.
Polynomial
Drag the colored dots on the x-axis to move roots.
Properties
| Degree | -- |
| Roots | -- |
| Factored | -- |
| y-intercept | -- |
| Leading a | -- |
| End behavior | -- |
The Math Behind It
Polynomial Basics
- Factored form: f(x) = a(x-r₁)(x-r₂)...(x-rₙ)
- Each r is a root (zero) where the graph crosses the x-axis
- Degree n = number of roots (counting multiplicity)
- y-intercept = f(0) = a·(-r₁)(-r₂)...(-rₙ)
Leading Coefficient
- a > 0: right side goes up
- a < 0: graph flips vertically
- |a| > 1: graph stretches vertically
- |a| < 1: graph compresses vertically
End Behavior
- Even degree, a > 0: both ends go up ↑↑
- Even degree, a < 0: both ends go down ↓↓
- Odd degree, a > 0: left down, right up ↓↑
- Odd degree, a < 0: left up, right down ↑↓
Try This
- Drag two roots to the same spot — double root (touches but doesn't cross)
- Make a negative — entire graph flips
- Try Quintic — see 4 turning points
- Click Animate — watch leading coefficient sweep
You're crushing it!