how do you find intersections with the functions?

Question

I understand parametric equations for the most part, but i always have trouble with finding their intersection points. I would be glad for a second opinion.

Thanks so much!

Answer 1

Two graphs intersect where their equations are equal.  Thus, the graph f(x) intersects with the graph g(x) where f(x)=g(x).

Upon setting the equations equal to each other, solve for x.  With the x-value, you can then substitute it back into either function to solve for the y-value.

Answer 2

If you are given two functions, let say f(x) and g(x), then their point (or points) of intersection (x₀₎ can be found by solving the equation   f(x₀) = g(x₀). The variable x can be given in a parametric fom x = x(t), where t is a parameter. If f(x) and g(x) are polynomials or transcedent functions, then finding the points of intersection may not be an easy problem. Then you have to use approximation or some numerical methods.

These are just very common comments. We can be more specific if the problem is specified. If you have other questions, I am ready to respond. Good luck!