Mathematics

Difference tables reveal the hidden pattern in polynomial sequences: each time you subtract consecutive terms, you drop down one level of complexity. For a quadratic, the first differences won't be constant (that's linear), but the second differences will be—and that constant tells you everything about the parabola's curvature. Build your table by computing $f(x)$ at each point, then systematically subtract pairs to watch the pattern emerge.

Difference tables reveal the hidden pattern in polynomial sequences: each time you subtract consecutive terms, you drop down one level of complexity. For a quadratic, the first differences won't be constant (that's linear), but the second differences will be—and that constant tells you everything about the parabola's curvature. Build your table by computing $f(x)$ at each point, then systematically subtract pairs to watch the pattern emerge.