Algebra Know-It-ALL

Positive/negative square root

The second of the three relations we evaluated in Chap. 13 took the positive or negative
square root of x,as follows:

y=±(x1/2)

Figure 14-5 shows some points for this relation, along with the curve that connects them. This
curve is called a parabola. It is characteristic of quadratic equations, which we’ll study in Part 3.

Nonnegative square root

The third relation we looked at in Chap. 13 was the same as the second one, but without the
negative values of y. It involved taking the nonnegative square root:

y=x1/2

Some points for this relation are plotted in Fig. 14-6, along with the curve that connects them.
It appears as the nonnegative half of the curve in Fig. 14-5.

Are you confused?

How many points must you plot before you truly know what the graph of a relation looks like? The best
answer is, “It depends.” With simple relations such as those in this chapter, a few points are enough.
With more complicated relations, you might have to plot many points before the complete graph can be

Three Relations 227

–6 –2–4 246

2

4

6

–2

–4

–6

x

y

(–5,–3)

(0,2)

(4,6)

Figure 14-4 Cartesian graph of the relation y=x+ 2.