Graphing Parametric Equations

Question 1

Which graph represents the parametric equations x(t) = t – 4 and y(t) = t2 + 5 for –1 ≤ t ≤ 2?

Revolt · Accepted Answer

On a coordinate plane, a curve starts at (negative 5, 6), curves down to (negative 4, 5), and then curves up to (negative 2, 9).

Question 2

Which graph represents the parametric equations x = t2 + 2t and y = –t, where –4 ≤ t ≤ 1?

Revolt · Accepted Answer

On a coordinate plane, a curve starts at (3, negative 1), curves up through (0, 0) to (negative 1, 1), and curves up through (0, 2) and (3, 3).

Question 3

A soccer ball on the ground was kicked with an initial velocity of 35 ft/sec at an elevation angle of 40°. Create a set of parametric equations to model the path of the soccer ball. Approximately how far had the soccer ball traveled when it hit the ground?

Revolt · Accepted Answer

38 feet

Question 4

Eliminate the parameter in the equations x = cos(t) – 5 and y = 3sin(t) + 6. How can the rectangular equation be described?

Revolt · Accepted Answer

ellipse

Question 5

Consider the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2. What is the rectangular form?

Revolt · Accepted Answer

StartFraction (x + 3) squared Over 16 EndFraction + StartFraction (y minus 2) squared Over 25 EndFraction = 1

Question 6

An animation features an airplane flying in a straight line across the screen from (0, 10) to (45, 160) in 5 seconds. Which parametric equations represent the onscreen path of the airplane?

Revolt · Accepted Answer

x(t) = 9t and y(t) = 30t + 10

Question 7

A coach throws a football from a height of 4 feet with an initial velocity of 59 feet per second at an elevation angle of 45°. Which parametric equations represent the path of the football?

Revolt · Accepted Answer

x(t) = 59cos(45o)t and y(t) = –16t2 + 59sin(45o)t + 4

Question 8

Eliminate the parameter in the equations y = t + 2 and x = . How can the rectangular equation be described?

Revolt · Accepted Answer

quadratic

Question 9

What is the rectangular form of the parametric equations x = 4 cos t and y = 5 sin t, where 0 ≤ t ≤ 2π?

Revolt · Accepted Answer

StartFraction x squared Over 16 EndFraction + StartFraction y squared Over 25 EndFraction = 1

Question 10

A soccer ball on the ground is kicked with an initial velocity of 37 feet per second at an elevation angle of 70°. Which parametric equations represent the path of the soccer ball?

Revolt · Accepted Answer

x(t) = 37cos(70o)t and y(t) = –16t2 + 37sin(70o)t

Graphing Parametric Equations Answers

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