AnswersPrecalculusGraphing Parametric Equations

Graphing Parametric Equations — Quiz Answers

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A swimmer enters the water and swims in a straight line at 54 meters per minute. Another swimmer enters the water 3 minutes later, swimming in the same direction at 74 meters per minute. Which parametric equations could model the swimmers' paths from the time the second swimmer entered the water?

A
x times t is equal to 54 t and y times t is equal to 74 times open paren t plus 3 close paren
B
x times t is equal to 54 times open paren t plus 3 close paren and y times t is equal to 74 t
C
x times t is equal to 54 t and y times t is equal to 74 times open paren t minus 3 close paren
D
x times t is equal to 54 times open paren t minus 3 close paren and y times t is equal to 74 t
2
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Eliminate the parameter in the equations y is equal to t plus 2 and x is equal to t raised to the 1 half power How can the rectangular equation be described?

A
linear
B
cubic
C
quartic
D
quadratic
3

Which graph represents the parametric equations x times t is equal to t minus 4 and y times t is equal to t squared plus 5 for negative 1 is less than or equal to t comma t is less than or equal to 2 ?

A
Image with description On a coordinate plane, a curve starts at (negative 5, 4), curves up to (negative 4, 5), and then curves down to (negative 2, 1).
B
Image with description 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).
C
Image with description On a coordinate plane, a curve starts at (negative 3, 6), curves down to (negative 4, 5), and curves up to (negative 6, 9).
D
Image with description On a coordinate plane, a curve starts at (negative 3, 4), curves up to (negative 4, 5), and curves down to (negative 6, 1).
4

Which graph represents the parametric equations x is equal to 3 t and y is equal to 1 half t cubed minus 1 , where negative 2 is less than or equal to t comma t is less than or equal to 3 ?

A
Image with description On a coordinate plane, a curve starts at (negative 9, 13), curves down through (negative 3, 0) to inflection point (0, negative 1), and then curves down to (6, negative 5).
B
Image with description On a coordinate plane, a curve starts at (6, 3), curves down through (4, 0) to inflection point (0, negative 1), and curves down through (negative 8, negative 10).
C
Image with description On a coordinate plane, a curve starts at (negative 6, negative 5), goes through (negative 4, negative 2) to inflection point (0, negative 1), and then curves up through (3, 0) to (9, 13).
D
Image with description On a coordinate plane, a curve starts at (negative 6, 3), curves down through (negative 4, 0), has inflection point (0, negative 1), and curves down through (8, negative 10).
5

Which rectangular equation represents the parametric equations x is equal to t raised to the 1 half power and y is equal to 4 t ?

A
y is equal to 1 fourth x squared , for x is greater than or equal to 0
B
y is equal to 4 x squared , for x is greater than or equal to 0
C
y is equal to 1 over 16 x squared , for x is greater than or equal to 0
D
y is equal to 16 x squared , for x is greater than or equal to 0
6

What is the rectangular form of the parametric equations x is equal to 4 cosine t and y is equal to 5 sine t , where 0 is less than or equal to t comma t is less than or equal to 2 pi ?

A
the fraction with numerator x squared and denominator 16 plus the fraction with numerator y squared and denominator 25 is equal to 1
B
the fraction with numerator x squared and denominator 25 plus the fraction with numerator y squared and denominator 16 is equal to 1
C
the fraction with numerator x squared and denominator 5 plus the fraction with numerator y squared and denominator 4 is equal to 1
D
the fraction with numerator x squared and denominator 4 plus the fraction with numerator y squared and denominator 5 is equal to 1
7

Which rectangular equation is formed by eliminating the parameter? y is equal to t cubed x is equal to t plus 5

A
y is equal to x cubed minus 15 x squared plus 75 x minus 125
B
y is equal to x cubed minus 125
C
y is equal to x cubed minus 5 x squared plus 25 x minus 125
D
y is equal to x cubed plus 125
8

Consider the parametric equations x is equal to 4 cosine t minus 3 and y is equal to 5 sine t plus 2 What is the rectangular form?

A
the fraction with numerator open paren x minus 3 close paren squared and denominator 16 plus the fraction with numerator open paren y plus 2 close paren squared and denominator 25 is equal to 1
B
the fraction with numerator open paren x plus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 5 is equal to 1
C
the fraction with numerator open paren x plus 3 close paren squared and denominator 16 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 25 is equal to 1
D
the fraction with numerator open paren x minus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y plus 2 close paren squared and denominator 5 is equal to 1
9

Which graph represents the parametric equations x is equal to t squared plus 2 t and y is equal to negative t , where negative 4 is less than or equal to t comma t is less than or equal to 1 ?

A
Image with description On a coordinate plane, a curve starts at (negative 1, negative 1) and curves up through (0, 0) and (8, 2).
B
Image with description On a coordinate plane, a curve starts at (negative 1, 1) and curves down through (0, 0) and (8, negative 2).
C
Image with description On a coordinate plane, a curve starts at (3, 1), curves down through (0, 0) to (negative 1, negative 1), and then curves down through (0, negative 2) to (8, negative 4).
D
Image with description 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).
10

Eliminate the parameter in the equations x is equal to cosine of t minus 5 and y is equal to 3 sine t plus 6 How can the rectangular equation be described?

A
noncircular ellipse
B
parabola
C
circle
D
hyperbola

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