CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 10. Polar and Parametric Equations

Notice how when these partial graphs are examined there is no intersection at anything besidest=±2 and the points
(2, 2) and (-2, -2) While the paths of the graphs intersect in four places, they intersect at the same time only twice.

2. First check to see if the point (-2, 6) produces a matching time for the original function.

TABLE10.3:

− 2 =t^2 − 10

8 =t^2

± 2

√

2 =t

6 = 2 t− 4

20 =t

The point does not live on the original function. Now, you must check to see if it lives on the inverse.

TABLE10.4:

6 =t^2 − 10

± 4 =t

− 2 =t 2 − 6

4 = 2 t

8 =t

The point does not live on the inverse either.
3.x 1 = 4 t;y 1 =t^2 −16 The inverse is:

x 2 =t^2 − 16

y 2 = 4 t

Solve fortwhenx 1 =x 2 andy 1 =y 2.

4 t=t^2 − 16

0 =t^2 − 4 t− 16

t=^4 ±

√ 16 − 4 · 1 ·(− 16 )

2 =

4 ± 4

√

5

2 =^2 ±^2

√

5

The points that correspond to these two times are: