The parameterization of a parabola

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Question from Shawna, a student:

I am having problems finding the parameterization of a parabola. The question I was given is: Find the work done if a particle moves from the points (-2,4) to (1,1) along the parabola y=x^2, while subject to the vector force of F=(x^3y,x-y). So how would I start with finding the parameterization of a parabola?

Hi Shawna,

The parabola $y = x^2$ is the set of all points in the plane for which the y-coordinate is the square of the x-coordinate, that is $\{(x ,x^2)| x \in \mathbb{R}\}.$ Hence the parabola can be parameterized by $(x, x^2).$

Penny

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