Polynomials · Mathematics, chapter 2
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Quadratic polynomials — roots and vertex
conceptId: quadratic-explorer
Quadratic polynomials: roots and vertex
CBSE Class 10 Mathematics · Ch 2 §2.2 — the zeroes of a polynomial are exactly where its graph crosses the x-axis.
f(x) = 1.00x² − x − 2.00
- discriminant D = b² − 4ac
- 9.00
- roots (real)
- -1.000 , 2.000
- vertex
- (0.500, -2.250)
- check f(root)
- 0.000000 , 0.000000
What to notice: the yellow dots are the zeroes — the curve meets the x-axis exactly there, and the check row shows f(root) = 0. Push c up until D turns negative and the curve lifts off the axis: no real zeroes left.
Try this: set b = 0 and c = −4 with a = 1 — the roots are exactly ±2, the vertex sits on the y-axis. Then set c = 0 and watch one root slide to the origin.
10 further animations in the registries belong to other chapters.
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