# Points, Vectors, and Functions

### Topics

We can describe trajectories of things with parametric equations.

Before we go forward, we should review parabolas via Super Mario Brothers. When Mario jumps, we can parameterize his trajectory *d*(*x,y*) = *t* by writing *d*(*t*) = <*x*(*t*),*y*(*t*)>.

To graph this parametric equation, we graph a bunch of individual points. To find the coordinates of a point we take a *t* value and find the corresponding *x* and *y* values.

How do we know if Mario landed safely on the other side of the canyon? We need to know if point (x_{1},y_{1}) is on the trajectory.

We are going to reverse the graphing process. We'll start with point (x_{1},y_{1}) and find the *t*-value that produced it, if there is one.

To determine if a particular point (*x*,*y*) is on a parametric graph we need to find a single value of the parameter *t* that produces the correct *x*- and *y*-values at the same time.