Question: Let $ f(x) $ be a cubic polynomial modeling genetic trait inheritance in a plant species, satisfying $ f(1) = -6 $, $ f(-1) = 2 $, $ f(2) = 12 $, and $ f(0) = -4 $. Find $ f(3) $.

Wed, 06 May 2026 16:37:40 +0000

**Unlocking Plant Genetics: The Hidden Patterns Behind Inherited Traits** Curiosity about how plants pass down characteristics—like yield, color, or resistance—drives growing interest among home gardeners, researchers, and agricultural innovators. At the core of this inquiry lies mathematical modeling: using cubic polynomials to map traits across generations. When modelers define f(x) as a cubic polynomial reflecting genetic inheritance, using real-world data points creates a powerful, precise expression that aligns with observable plant behavior. The equation, grounded in proven math, reveals how variables like environmental stress or selective breeding shape inherited outcomes—making it both scientifically valuable and naturally searchable as people explore bionic breeding trends, gene mapping, and sustainable farming solutions. This cubic polynomial satisfies four specific conditions: f(1) = -6, f(-1) = 2, f(2) = 12, and f(0) = -4. Solving for f(3) reveals not just a number—but insight into biological prediction models increasingly relevant in agricultural innovation and genetic research. ---