Introduction to Loci in the Plane
The most interesting sets of points to graph are collections of points that are defined by an equation. We call such a graph the locus of the equation. We cannot give all the theory of loci here, but instead consider a few examples. See [SCH2] for more on this matter.
Examples
Example 1
Sketch the graph of {( x , y ): y = x ^{2} }.
Solution 1
It is convenient to make a table of values:
x 
y = x ^{2} 
−3 
9 
−2 
4 
−1 
1 
0 
0 
1 
1 
2 
4 
3 
9 
We plot these points on a single set of axes ( Fig. 1.19 ). Supposing that the curve we seek to draw is a smooth interpolation of these points (calculus will later show us that this supposition is correct), we find that our curve is as shown in Fig. 1.20 . This curve is called a parabola .
Example 2
Sketch the graph of the curve {( x , y ): y = x ^{3} }.
Solution 2
It is convenient to make a table of values:
x 
y = x ^{3} 
−3 
−27 
−2 
−8 
−1 
−1 
0 
0 
1 
1 
2 
8 
3 
27 
We plot these points on a single set of axes (Fig. 1.21). Supposing that the curve we seek to draw is a smooth interpolation of these points (calculus will later show us that this supposition is correct), we find that our curve is as shown in Fig. 1.22. This curve is called a cubic .
You Try It: Sketch the graph of the locus ∣ x ∣ = ∣ y ∣.

1
 2
Ask a Question
Have questions about this article or topic? AskPopular Articles
 Kindergarten Sight Words List
 First Grade Sight Words List
 10 Fun Activities for Children with Autism
 Definitions of Social Studies
 Signs Your Child Might Have Asperger's Syndrome
 Curriculum Definition
 Theories of Learning
 Child Development Theories
 A Teacher's Guide to Differentiating Instruction
 Netiquette: Rules of Behavior on the Internet