Mathematical Methods · quadratic functions · manipulative

Discriminant and roots

Δ = b² − 4ac decides how many times the parabola meets the x-axis — two, one (tangent), or none.

y = ax² + bx + c real roots

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Discriminant

Δ = b² − 4ac
—

Coefficients

1
-3
2

a ≠ 0 (clamped) — otherwise it is not a quadratic.

Working