Introduction to Parametric Equations

AP Calculus · Axiom Academy

INTRO Introduction to Parametric Equations What if we described motion in a completely new way? You've spent time studying functions where y depends on x: . But what if we need to describe something more complex, like the path of a projectile, the motion of a planet, or a rollercoaster? These involve movement in time. This is the heart of parametric equations. Instead of one equation , we use TWO equations: where t is the parameter (usually representing time) As t changes, the point (x, y) traces out a curve. We're describing BOTH the x and y coordinates independently in terms of time. Real-World Example: Projectile Motion When you throw a ball at an angle, it doesn't follow a simple y = f(x) function. Instead: Here t is time in seconds, v₀ is initial velocity, θ is launch angle, and g is gravity. Parametric equations make this crystal clear! Each piece of motion—horizontal and vertical—has its own equation in terms of time. Why Parametric Equations Are Powerful In the next modules, you'll learn how to work with parametric equations—taking derivatives, finding arc length, and understanding motion in the plane. Let's dive in!

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