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Investigate the family of curves defined by the parametric equations $ x = t^2 $, $ y = t^3 - ct $. How does the shape change as $ c $ increases? Illustrate by graphing several members of the family.
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Calculus 2 / BC
Chapter 10
Parametric Equations and Polar Coordinates
Section 1
Curves Defined by Parametric Equations
Parametric Equations
Polar Coordinates
Campbell University
Harvey Mudd College
Idaho State University
Lectures
16:57
In mathematics, a graph is a representation of a set of objects where some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" or "nodes", and the relations between them are represented by mathematical abstractions called "edges" or "arcs". The basic notion of a graph was developed by the 17th-century French mathematician Pierre de Fermat, and the term "graph" was coined by the 19th-century mathematician James Joseph Sylvester. The more general mathematical concept of a graph "in which any kind of relation between elements of the set is expressed as an edge, is called a network" (Kolmogorov, "1956, p. 111"). In other words, an undirected graph is a graph in which the edges have no direction associated with them. The most familiar examples of graphs are the graphs of equations. In general, the vertices of a graph can represent concepts and the edges can represent real-valued functions on the concepts, so one can speak of the graph as a function's graph or of the edge as a function's edge.
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Polar coordinates are a two-dimensional coordinate system that specifies a point in terms of distance from a reference direction (the pole) and angle from a reference direction (the polar axis).
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$$ \begin{array}{l}{\text …
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Investigate the family of …
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Graph several members of t…
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the problem is investigate the family of curves you find about the parametric equations actually boarded his square. Why go to this Cuban minus city? How does the shape change? As said increases illustrated by graphing several members of the family? Little Cat's a graph here. This curve is sick or too negative one. And this one this they could. Cyril, this is safe. What? You three. This is sick with selling so we can see that one sees last and cereal. The function is an increasing function I see is the greatest and Cyril, the functions of first is secreting on, Then increasing and I see increases. We can see that the local minimum while you is getting smaller and smaller.
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