Graphing Parametric Equations — Quiz

Question 3 • Precalculus

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 ?

Answer

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).

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).

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).

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).

Explanation

At t = −1, the equations give (x, y) = (−5, 6). At t = 0, they give (−4, 5), and at t = 2, they give (−2, 9). Since y = t² + 5 decreases until t = 0 and then increases, the curve passes down to (−4, 5) and then back up, matching the graph that starts at (−5, 6): choice B.

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