Question: A science fiction writer imagines a cubic polynomial $ h(x) $ that models the trajectory of a spaceship, satisfying $ h(1) = -6 $, $ h(2) = -10 $, $ h(3) = -14 $, and $ h(4) = -18 $. Find $ h(0) $.

Tue, 05 May 2026 07:30:49 +0000

**Question: A science fiction writer imagines a cubic polynomial $ h(x) $ that models the trajectory of a spaceship, satisfying $ h(1) = -6 $, $ h(2) = -10 $, $ h(3) = -14 $, and $ h(4) = -18 $. Find $ h(0) $.** A science fiction trajectory often unfolds in elegant, predictable patterns—even when shaped by imagination. When a writer crafts a cubic polynomial to model a spaceship’s path, subtle mathematical rules emerge, turning abstract fiction into believable science. This cubic function, defined by four precise data points, follows a trajectory that deepens in complexity with each integer x-value—descending steadily, like a spacecraft descending through layered atmospheric zones in a dystopian future. The sequence $ h(1) = -6 $, $ h(2) = -10 $, $ h(3) = -14 $, $ h(4) = -18 $ reveals a consistent decrease of 4 units across consecutive x-values. This pattern suggests a linear decrease embedded within a cubic framework—implying that while the function is cubic, it exhibits strong first-order behavior over a few points. Now, the key question becomes: can we determine $ h(0) $—the spaceship’s trajectory at launch—with precision? **Understanding the Polynomial and Its Hidden Pattern**