Graphing Parametric Equations — Quiz

Question 4 • Precalculus

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 ?

Answer

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).

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).

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).

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).

Explanation

At the parameter endpoints, t = −2 gives (x, y) = (−6, −5), and t = 3 gives (9, 12.5), approximately (9, 13). As t increases, both x = 3t and y = ½t³ − 1 increase, and the curve has an inflection point at t = 0, or (0, −1). Choice C has the matching endpoints and rising shape.

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