Question 1

Which of the following best describes a parametric equation?

Accepted Answer

An equation that expresses $$x$$ and $$y as $$functions of a third variable, called the parameter.

Question 2

Given the parametric equations $$x(t) = t^2$ and y(t$$) = $$t^3$$, for $$-2 \leq t \leq 2$$, which of the following points lies on the curve?

Accepted Answer

$$(1, 1)$$

Question 3

If $$x(t) = 2t - 1$$ and $$y(t) = 2t$$, what is the Cartesian equation relating $$x$$ and $$y$$?

Accepted Answer

$$y = x + 1$$

Question 4

Which of the following is a correct interpretation of the orientation of a parametric curve?

Accepted Answer

The direction in which the curve is traced as the parameter increases.

Question 5

Suppose $$x(t) = t^2$ and y(t$$) = $$t^2 + 1$ for -2$$ \leq t \leq 2$$. Which of the following is the correct Cartesian equation?

Accepted Answer

$$y = x + 1$$

Question 6

Given $$x(t) = t$$ and $$y(t) = t^2$, what type of curve is represented by these parametric equations?

Accepted Answer

A parabola opening upwards.

Question 7

If $$x(t) = \cos t$$ and $$y(t) = \sin t$$ for $$0 \leq t \leq 2\pi$$, what is the orientation of the curve?

Accepted Answer

Counterclockwise around the unit circle.

Question 8

A car travels along a path described by $$x(t) = 3t$$ and $$y(t) = 2t + 1. At$$ $$t = 2$$, what is the position of the car?

Accepted Answer

$$(6, 5)$$

Question 9

Given $$x(t) = t^2$ and y(t$$) = $$t^3$$, which of the following statements is true about the orientation as $$t$$ increases from $$-2 to$$ $$2$$?

Accepted Answer

The curve starts at $$(4, -8)$$ and ends at $$(4, 8).$$

Question 10

If $$x(t) = t$$ and $$y(t) = t + 2$$, which of the following is the correct Cartesian equation?

Accepted Answer

$$y = x + 2$$

Question 11

A projectile is launched such that its position is given by $$x(t) = 10t$$ and $$y(t) = -5t^2$ + 20t. $$What is the position of the projectile at $$t = 2$$?

Accepted Answer

$$(20, 20)$$

Question 12

Which of the following is NOT a feature of parametric equations?

Accepted Answer

They always represent straight lines.

Question 13

Given $$x(t) = t^2$ and y(t) = 2t$, eliminate the parameter to find the Cartesian equation.

Accepted Answer

$$y^2 = 4x$

Question 14

If $$x(t) = t$$ and $$y(t) = t^2$ - 1$$, what is the vertex of the parabola described by these equations?

Accepted Answer

$$(0, -1)$$

Question 15

A runner's path is modeled by $$x(t) = 5t$$ and $$y(t) = 3t + 2. $$How far has the runner traveled in the $$x-$$direction after 4 seconds?

Accepted Answer

$$20$$

Graphing Parametric Equations: Introduction and Practice

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