๐ Visual Concept Diagrams & Figures
Interactive Graphics
Parabola Geometry & Real Roots
Geometric Analysis of Discriminant D = bยฒ - 4ac
The discriminant D = bยฒ - 4ac determines how the parabola y = axยฒ + bx + c intersects the x-axis: D > 0 yields two real roots (green curve), D = 0 touches at a single vertex x = -b/(2a) (amber curve), and D < 0 floats with no real roots (rose curve).