The Layer That Settles Names the Family

You'll learnto tell a linear function from a quadratic one by subtracting a table of outputs.

A linear function has one rate of change and keeps it on every interval. A quadratic has a rate that drifts, but drifts at a constant rate of its own. Subtracting a table once, then twice, turns that difference into a test with a yes-or-no answer.

8 STEPS · 6 QUICK CHECKS · Δ · Δ² · EQUAL SPACING · v2

subtract once for a line, twice for a parabola

Before you start

What you're looking at

A table of outputs with subtraction arrows building a row of first differences, then second differences.

The question

Which row of differences finally stops changing — the first, or the second?

Watch for

Whether the first differences stay equal (a line) or the second differences do (a parabola).

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