Practice!

Sample Problem

Sketch the curve represented by x=t-1 and y=t2.

Solution

The parametric equations x=t-1 and y=t2 yield the following (x, y) points [this is just a sample of points to get an idea of what the general graph looks like]:

t=-2 – x=-3; y=4 (-3, 4)

t=-1 – x=-2; y=1 (-2, 1)

t=0 – x=-1; y=0 (-1, 0)

t=1 – x=0; y=1 (0, 1)

t=2 – x=1; y=4 (1, 4)

Plot these points in order of increasing t values to obtain the orientation of the curve. If a particle were moving on this curve for example, it would go from (-1, 0) to (0, 1) and towards the right side of the parabola.