10.4. Parametric Inverses http://www.ck12.org
Answers:
- The parameterized function is:
x 1 =t
y 1 =t^2 +t− 4The inverse is:
x 2 =t^2 +t− 4
y 2 =tTo find where these intersect, setx 1 =x 2 andy 1 =y 2 and solve.
t=t^2 +t− 4
t^2 = 4
t=± 2You still need to actually calculate the points of intersection on the graph. You can tell from the graph in Example
C that there seem to be four points of intersection. Sincetcan mean time, the question of intersection is more
complicated than simply overlapping. It means that the points are at the samexandycoordinate at the same
time. Note what the graphs look like when− 1. 8 <t< 1. 8.
Note what the graphs look liket> 2 .2 ort<− 2. 2