sheldonrocks97 said:Homework Statement
Find the parametric equations for the portion of the parabola y=x^2 from
(-1,1) to (3,9)
Homework Equations
None that I know of.
The Attempt at a Solution
Using knowledge of parametric equations I am not sure how to start. My teacher never went over this in class and she assigned it as homework. How do I start?
Parametric equations for a parabola are equations that express the coordinates of points on the parabola in terms of one or more parameters. In this case, the parameters would be represented as t, and the equations would be x=t and y=t^2.
To graph parametric equations for a parabola, you will need to plot points by substituting different values of t into the equations. Once you have enough points, you can connect them to create the graph of the parabola. Make sure to choose a range of values for t that will cover the portion of the parabola you want to graph.
The parameter t in parametric equations for a parabola represents the independent variable that allows us to trace out the curve. It can be thought of as the "time" variable, as it controls the direction and speed of movement along the parabola.
Yes, parametric equations for a parabola can be used to solve real-world problems. For example, they can be used to model the trajectory of a thrown object or the shape of a satellite's orbit around a planet. These equations can also be used in engineering and physics to design and analyze various systems.
Parametric equations for a parabola can provide a more precise and flexible representation of the parabola compared to traditional equations. They also allow for easier manipulation and analysis of the curve. Additionally, parametric equations can be used to model more complex and dynamic situations, making them a valuable tool in various fields of science and engineering.