Parameterize part of a Parabola

Thread starter getty102
Start date Jan 13, 2012
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Parabola Parameterize

In summary, parameterization in relation to a parabola refers to expressing the coordinates of points on the parabola in terms of a parameter, allowing for a more general representation of its shape and easier manipulation and analysis. A parabola can be parameterized by substituting the parameter for <i>x</i> in the general formula. Parameterizing a parabola allows for greater flexibility and the ability to find specific points on the parabola. Any point on a parabola can be represented using a parameter, and the direction and orientation of the parabola remain unchanged when parameterized.

Jan 13, 2012

getty102

Homework Statement

Find a parametric equation for a part of a parabola.

Given:
y=-2x²
initial point: (-2,-8)
terminal point: (1,-2)

Homework Equations

x(t)=a+t(c-a)
y(t)=b+t(d-b)

The Attempt at a Solution

x(t)=-2+t(1-(-2))
=3t-2
y(t)=-8+t(-2-(-8))
=6t-8

I'm not sure where to go from there.

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Jan 13, 2012

jedishrfu

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Insights Author

dont you need to plug the x(t) into the y=-2x^2 to get y(t)

Related to Parameterize part of a Parabola

1. What is the definition of parameterization in relation to a parabola?

Parameterization in relation to a parabola refers to the process of expressing the coordinates of points on the parabola in terms of a parameter, usually denoted as t. This allows for a more general representation of the parabola's shape and allows for easier manipulation and analysis.

2. How is a parabola parameterized?

A parabola can be parameterized by using the general formula for a parabola, y = ax^2 + bx + c, and substituting t for x to get y = at^2 + bt + c. This allows for the coordinates of points on the parabola to be expressed in terms of t.

3. What is the significance of parameterizing a parabola?

Parameterizing a parabola allows for a more general and flexible representation of the parabola's shape. It also allows for easier manipulation and analysis of the parabola, as well as the ability to find specific points on the parabola using the parameter t.

4. Can any point on a parabola be represented using a parameter?

Yes, any point on a parabola can be represented using a parameter. The parameter t can take on any real value, and therefore, can be used to express any point on the parabola.

5. How is the direction and orientation of a parabola affected by its parameterization?

The direction and orientation of a parabola remains unchanged when it is parameterized. The only difference is that the coordinates of points on the parabola are expressed in terms of a parameter, instead of the traditional x and y coordinates.