A Path Is a Journey, Not Just a Shape

You'll learnto see a parametric path as a journey with a start, a direction, and an extent.

One parameter drives both coordinates at once, so a parametric function arrives as a trip, not just a curve: it has a starting point, a direction of travel, and an extent the interval sets. Eliminating the parameter names the shape the trip rides on — and quietly discards the other three. Watch what survives that trade, and what does not.

8 STEPS · 6 QUICK CHECKS · START · DIRECTION · EXTENT · v2

Unit 4 is not assessed on the AP exam; schools include it where local requirements ask.

arrowheads show the direction of travel

Before you start

What you're looking at

Two machines sharing one slider t: t drives x(t) and y(t), and the two outputs form one moving point.

The question

As t advances, where is the point and which way is it heading?

Watch for

t as the shared driver — not one of the axes — shown at three separate values before the motion turns continuous.

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