Question

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

Answer 1

Which graph indeed?

Eliminate the parameter:

x = t - 4 ⇒ t = x + 4

⇒ y = t² + 5 = (x + 4)² + 5

which is the equation of a parabola with vertex at (-4, 5) and opening upwards, plotted with domain

-1 ≤ t ≤ 2 ⇒ -1 ≤ x + 4 ≤ 2 ⇒ -5 ≤ x ≤ -2

Answer 2

it is c

Explanation: