Solve Quadratic Equations Using the Quadratic Formula (Interactive GeoGebra)

① This GeoGebra example demonstrates how to solve quadratic equations using the quadratic formula, with interactive controls that show how changing coefficients affects the roots. ② The core mathematical concepts include the standard form ax²+bx+c=0, the discriminant Δ=b²-4ac, and the quadratic formula x=(-b±√Δ)/(2a), covering both real and complex roots. ③ Construction highlights: the Random command generates random coefficients a, b, c; the If command checks the sign of the discriminant to compute real or complex roots; multiple text objects (text1 to text21) display the equation, discriminant, roots, and solution steps; a button (button1) regenerates a random equation; sliders or input fields (s1, s2, etc.) allow manual coefficient adjustment; objects l, l1, l2, l3 store roots or intermediate results, while nr, nr1 etc. hold numeric outputs. ④ Suitable for upper middle school to high school students and math teachers for classroom demonstrations or self-study, reinforcing the quadratic formula, discriminant analysis, and the geometric interpretation of roots.