Investigation 2: Solving Parametric Equations
Solve parametric equations in Grade 10 math. Eliminate the parameter t to find the rectangular equation, trace paths point by point, and analyze motion described by x(t) and y(t).
Key Concepts
New Concept When two variables are expressed in terms of a third variable, the equations used are called parametric equations .
What’s next Next, you'll use this concept to model real world scenarios, like painting a house and hitting a golf ball, by plotting their paths over time.
Common Questions
What are parametric equations?
Parametric equations express x and y as separate functions of a third variable t (the parameter). For example, x = 2t and y = t² describe a curve where each t value gives a (x, y) point.
How do you eliminate the parameter to get a rectangular equation?
Solve one parametric equation for t and substitute into the other. For x = 2t, y = t²: t = x/2, so y = (x/2)² = x²/4. The rectangular form is y = x²/4.
What is the advantage of parametric form over rectangular equations?
Parametric equations describe direction, speed, and position over time, not just the curve shape. They can represent curves that fail the vertical line test and model projectile motion, circular paths, and more.