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@andrea.cordeiro.d: #feliznavidad #CapCut

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Friday 06 November 2026 12:14:05 GMT
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The sign of a quadratic, in one single journey ✨ Everything starts from ax² + bx + c with a > 0: the parabola opens upward. Its sign depends on one number only, the discriminant Δ = b² − 4ac. A comet leaves Δ and visits all three cases. 🔹 Δ > 0: two distinct roots, r₁ = (−b − √Δ)/(2a) and r₂ = (−b + √Δ)/(2a). The parabola crosses the x-axis at two points. The quadratic is positive outside the roots and negative between them. → ax² + bx + c > 0 ⟺ x ∈ (−∞, r₁) ∪ (r₂, +∞) 🔹 Δ = 0: one double root, r = −b/(2a). The parabola touches the x-axis at a single point. The quadratic is positive everywhere, except at r, where it equals zero. → x ∈ (−∞, r) ∪ (r, +∞) 🔹 Δ < 0: no real root. The parabola stays above the x-axis. → x ∈ ℝ 🔄 What if a < 0? The parabola flips: same roots, opposite signs. For Δ > 0, the quadratic is positive only between the roots. For Δ ≤ 0, the inequality has no solution. 💡 Key idea: every sign in the table is the vertical projection of a piece of the curve. Reading the parabola means reading the sign table. An animation built step by step, with rigor and beauty as the only rules. #maths #math #quadratic #parabola #animation
The sign of a quadratic, in one single journey ✨ Everything starts from ax² + bx + c with a > 0: the parabola opens upward. Its sign depends on one number only, the discriminant Δ = b² − 4ac. A comet leaves Δ and visits all three cases. 🔹 Δ > 0: two distinct roots, r₁ = (−b − √Δ)/(2a) and r₂ = (−b + √Δ)/(2a). The parabola crosses the x-axis at two points. The quadratic is positive outside the roots and negative between them. → ax² + bx + c > 0 ⟺ x ∈ (−∞, r₁) ∪ (r₂, +∞) 🔹 Δ = 0: one double root, r = −b/(2a). The parabola touches the x-axis at a single point. The quadratic is positive everywhere, except at r, where it equals zero. → x ∈ (−∞, r) ∪ (r, +∞) 🔹 Δ < 0: no real root. The parabola stays above the x-axis. → x ∈ ℝ 🔄 What if a < 0? The parabola flips: same roots, opposite signs. For Δ > 0, the quadratic is positive only between the roots. For Δ ≤ 0, the inequality has no solution. 💡 Key idea: every sign in the table is the vertical projection of a piece of the curve. Reading the parabola means reading the sign table. An animation built step by step, with rigor and beauty as the only rules. #maths #math #quadratic #parabola #animation
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You post regularly, but the inquiries are still not coming in? The problem isn't always the algorithm. Most small businesses make a few costly mistakes that push potential customers away before they ever make contact. ❌ Stop posting without a strategy. ❌ Stop ignoring customer inquiries and follow-ups. ❌ Stop selling all the time without providing value. Instead: ✅ Build trust through testimonials and real results. ✅ Engage with your audience and start meaningful conversations. ✅ Focus on lead generation, follow-ups, and conversion strategies. Remember: Marketing is not about chasing customers; it's about attracting them. If your business needs help generating more leads, increasing visibility, and turning followers into paying customers, send me a DM today. 📩 DM for Social Media Management 📞 0706510908 #SmallBusinessMarketing #DigitalMarketingTips #BusinessGrowth #LeadGeneration #SocialMediaMarketing
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