Live Calculator & PlotterView in 3D Mind-Map

50-Formula Live Calculator & 2D Function Graph Plotter Lab

Enter parameters or drag sliders to compute instant numerical answers and plot 2D curves, unit circles, vectors, and probability distributions.

🧮 Live Formula Calculator & Plotter
Coeff a
Coeff b
Constant c
D=(−3)2−4(1)(−4)=25.00D = (-3)^2 - 4(1)(-4) = 25.00
Roots x₁, x₂
4.00, -1.00
Discriminant D
25.00 (실근 2)
Vertex
(1.50, -6.25)
#A04 · Algebra & Number TheoryView Full Encyclopedia

Quadratic Formula & Discriminant

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
ax2+bx+c=0(D=b2−4ac)ax^2 + bx + c = 0 \quad (D = b^2 - 4ac)

Solves any quadratic equation directly from its coefficients via completing the square, while the discriminant D = b² - 4ac classifies real, repeated, or complex roots.

AI & Coding Real-World Use

3D Ray-Sphere intersection in ray tracing shaders and projectile trajectory impact time calculation

const D = b*b - 4*a*c; const x1 = (-b + Math.sqrt(D)) / (2*a);

Quick Switch Formula Calculators