Quadratic Formula Calculator
Calculates the exact roots of quadratic polynomial equations using the quadratic formula. Provides discriminant analysis (b² - 4ac) and parabola vertex coordinates.
PARAMETERS(3)
LOAD VERIFIED SCENARIO
ACTIVE COMPUTATION
Roots (x)
x₁ = 3, x₂ = 2
Two distinct real roots
Discriminant (Δ)
1
Vertex (h, k)
(2.5, -0.25)
Axis of Symmetry
x = 2.5
MATHEMATICAL FORMULA & GOVERNING PRINCIPLES
x = (-b ± √(b² - 4ac)) / (2a)
Where Δ = b² - 4ac is the discriminant. If Δ > 0 there are two distinct real roots; if Δ = 0 there is one real double root; if Δ < 0 there are two complex conjugate roots.
FREQUENTLY ASKED QUESTIONS (FAQ)
What does the discriminant tell you?
The discriminant (b² - 4ac) indicates the number and nature of roots. A positive value means two real solutions, zero means one repeated real solution, and a negative value means two complex solutions involving the imaginary unit i.
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