Consider the parametric equations below. x = t2 − 3, y = t + 1, −3 ≤ t ≤ 3 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b) Eliminate the parameter to find a Cartesian equation of the curve. for −2 ≤ y ≤ 4

Question

Consider the parametric equations below. x = t2 − 3, y = t + 1, −3 ≤ t ≤ 3 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.  (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −2 ≤ y ≤ 4

oobleck · Answer

eliminating t, we get t = y-1 so x = (y-1)^2 - 3 which is a parabola with its vertex at (-3,1) opening to the right