1. ## Quadratic & Linear Intersections

I have the following equations:

(Where d = distance, t = time)

1) d = 1.5 + 0.8t
2) d = 2.8 + 0.7t
3) d = 0.1t(t - 4.5)
4) d = 0.03t2 + 0.6t
5) d = 0.1t3 - 1.8t2 + 8.1t

I am asked to "find all of the intersections for all 5 functions for the domain [12, 14]".

I know how to find the intersections of a pair of equations individually, but I'm unsure how to tackle this question in relation to all five functions and the domain as a whole.

Some guidance would be much appreciated.

2. ## Re: Quadratic & Linear Intersections

Hey Fratricide.

The idea is very similar to the pair-wise case with one twist.

What you do is you do all pair-wise solutions and find all solutions that are common to all of them. If you don't find any common solution to all pair-wise solutions then it means that the system of equations is in-consistent just like the case when you have an inconsistent system in linear algebra.

Doing this efficiently without a computer is tough, but I would look at the linear and quadratic systems differently and then together.

Linear algebra allows us a way to do this in a generalized form but since you have quadratics, you will need to do this by first principles.

Mathematically this amounts to taking the intersection of all solutions given by all the pair-wise solutions (i.e. the solution to (x,y) where x != y and x,y = 1 to 5 in your case) and using this result as the solution of this system of equations.

3. ## Re: Quadratic & Linear Intersections

I do have a Casio Classpad 330 that I am able to use, although I don't know how to use it accurately for this problem. Is there anyone who's familiar with Classpads that can put me on the right track? (Again, I know how to find the intersecting point of two lines, but I don't know how to establish a domain.)

Also, could you elaborate on the process required to determine the solutions mathematically? Provide some examples, perhaps?