# Thread: Finding the formula with the parametric curve?

1. ## Finding the formula with the parametric curve?

"The parametric curve given by x = t - 2 and y = 2t + 1 for t ∈ ℝ is also the graph of a function f(x). Find the formula for f(x)."

First of all, I would like to know that are these curves on the x-y plane or the x,y,z-plane? As I was confused as to whether you would have to sketch out the curves with finding the answer. Moreover, the answer, 2x + 5 does not include values of t but the equations for the parametric curve do. What I don't understand there is how you're able to find the formula by using the parametric curve?

2. First of all, I would like to know that are these curves on the x-y plane or the x,y,z-plane?
On the x-y plane.

As I was confused as to whether you would have to sketch out the curves with finding the answer.
You don't have to. Here it is easier to solve the problem algebraically.

What I don't understand there is how you're able to find the formula by using the parametric curve?
You have to find such expression f(x) that when you substitute x = t - 2 into it, you get 2t + 1. In this case, it is easy because t and x can be expressed through each other. In particular, you can express t through x. When you substitute this expression of x for t in 2t + 1, you get the required f(x). If later you substitute t - 2 for x in this expression, you again get 2t + 1.

3. It's called "eliminating the parameter". Solve one of the equations in terms of $\displaystyle \displaystyle t$ and then substitute the result into the second equation.

$\displaystyle x = t - 2 \iff t = x + 2$

$\displaystyle y = 2t + 1 = 2(x + 2) + 1$

4. Originally Posted by cottontails
"The parametric curve given by x = t - 2 and y = 2t + 1 for t ∈ ℝ is also the graph of a function f(x). Find the formula for f(x)."

First of all, I would like to know that are these curves on the x-y plane or the x,y,z-plane? As I was confused as to whether you would have to sketch out the curves with finding the answer. Moreover, the answer, 2x + 5 does not include values of t but the equations for the parametric curve do. What I don't understand there is how you're able to find the formula by using the parametric curve?
Surely your textbook or class notes have enough examples that you could figure out the answers to most of the above questions yourself ....?