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# Loci in the Plane Help (page 2)

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By McGraw-Hill Professional
Updated on Aug 31, 2011

#### Example 3

Sketch the graph of the curve y = x 2 + x − 1.

#### Solution 3

It is convenient to make a table of values:

 x y = x 2 + x − 1 −4 11 −3 5 −2 1 −1 −1 0 −1 1 1 2 5 3 11

We plot these points on a single set of axes (Fig. 1.23). 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. 1.24. This is another example of a parabola.

Fig. 1.23

You Try It: Sketch the locus y 2 = x 3 + x + 1 on a set of axes.

The reader unfamiliar with cartesian geometry and the theory of loci would do well to consult [SCH2].

Fig. 1.24

Find practice problems and solutions for these concepts at Calculus Basics Practice Test.

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