Family Overview
In Plain Language
Topic 4.3 analyzes direction and rates of change for parametric planar motion.
- Horizontal direction: x(t) increasing moves right; decreasing moves left (4.3.A.1).
- Vertical direction: y(t) increasing moves up; decreasing moves down (4.3.A.1).
- Changing direction: motion direction can differ at different t values (4.3.A.2).
- Parametrizations: one curve can be traced different ways (4.3.A.3).
- Average rates: compute average ROC for x(t) and y(t); their ratio gives secant slope when avg ROC x != 0 (4.3.A.4).
Course scope only (Unit 4 additional topic; not on the AP Exam).
Why It Matters
Direction and average rates connect parametric graphs to motion language before lines/circles in 4.4.
How Families Can Help
- Ask: "Is x going up or down in value? What does that mean left/right?"
- Compare two t-intervals on the same path.
- Use a short table to justify direction claims.
What Not to Do
- Do not confuse position (4.2) with direction of travel.
- Do not divide by zero when average ROC of x is 0.
- Do not assume one parametrization is the only way to trace a curve.