Find a parameterization for each of the following curves.

a. The straight line segment from (3,2) to (-1,1).

b. The curve \(\displaystyle y=1-x^2\) from (3,-8) to (-2,-3).

I have no idea how to do this problem. Looks like a basic problem but I have no idea what parameterization means. Any help is appreciated!

Then I assume you immediately looked up "parameterization" or "parameter" in the index of your book and now know what it means!

A parameter or a curve is an additional variable, t, say such that both x and y are written in terms of that variable. Any one-dimensional object, such as a curve, can be written in terms of 1 parameter, any two-dimensional object, such as a surface, can be written in terms of two parameters. In effect, that's what "dimension" means.

But as long as y is a function of x, we can use "x" itself as parameter.

If \(\displaystyle y= 1- x^2\) we can take \(\displaystyle x= t\), \(\displaystyle y= 1- t^2\) with \(\displaystyle -3\le t\le t\).