Final answer:
To convert parametric equations to a Cartesian equation, eliminate the parameter by expressing it in terms of one variable and substituting it into the other equation. Calculators can aid in this process, and the converted Cartesian equation can be graphed using an equation grapher.
Step-by-step explanation:
To turn parametric equations into a Cartesian equation, you need to eliminate the parameter between the two parametric equations. Often, this involves expressing the parameter in terms of one of the variables and then substituting that expression into the other equation. For instance, if you have the parametric equations x = at and y = bt^2, you would solve the first equation for t to get t = x/a, and then substitute that into the second equation to get y = b(x/a)^2, which simplifies to y = bx^2/a^2, a Cartesian equation.
Using a calculator or computer can assist with this conversion, especially when dealing with more complex parametric equations. Some calculators have built-in functions to convert parametric to Cartesian equations, labeled under different function names depending on the calculator model.
For equation grapher tools, after converting the parametric equation to a Cartesian equation, you can input the Cartesian equation to graph polynomials and analyze the shape of the curve as constants are adjusted.