Parametric Equations and Their Graphs

This video introduces parametric equations, explaining their definition and how they differ from traditional equations. It uses projectile motion as an example to illustrate the application of parametric equations. The video also covers graphing techniques, showing how parametric equations can create unique plane curves. It provides examples of different parametric graphs, including trigonometric ones, and demonstrates how to graph these equations by hand. The video concludes with a preview of upcoming topics, such as converting parametric equations to rectangular form and using graphing calculators.

What is a parametric equation?

• An equation that cannot be graphed.

• An equation that is always linear.

• An equation that only involves X and Y.

• An equation that defines X and Y as functions of a third variable, usually T.

In parametric equations, what role does the parameter T play?

• It controls the values of X and Y and traces the curve direction.

• It is used to solve for Y.

• It is always a constant.

• It is used to solve for X.

How can the direction of a plane curve be indicated in parametric equations?

• By altering the parameter T.

• By using arrows along the curve.

• By changing the equation.

• By using different colors.

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What is the result of the parametric equations x = 2 - 3T and y = 1 - 2T?

• A line.

• A hyperbola.

• A parabola.

• A circle.

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What does the parametric equation x = t^2 and y = t represent?

• A line.

• A parabola.

• An ellipse.

• A circle.

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What is the significance of the unit circle in parametric equations?

• It helps in understanding circular motion.

• It is unrelated to parametric equations.

• It represents a line.

• It is used to solve linear equations.

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What is the graph of x = 4 cos(T) and y = 4 sin(T)?

• A triangle.

• A line.

• A circle.

• A square.

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When graphing parametric equations by hand, what is the first step?

• Select values of T within the given interval.

• Draw a random curve.

• Solve for X and Y.

• Use a graphing calculator.

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How do you determine the direction of a curve when graphing parametric equations?

• By plotting points in reverse order.

• By using arrows to show the direction as T increases.

• By changing the values of X and Y.

• By using a different parameter.

What is the result of graphing the parametric equations x = 4 cos(T) and y = 4 sin(T) over the interval from 0 to 2π?

• A circle centered at the origin.

• An ellipse.

• A line segment.

• A square.