Algebra Know-It-ALL

Part Three 531

the second function. Figure 30-3 shows the curves and the solution point. On both axes, each
increment represents 1 unit.

Question 28-3

Consider the system of equations we solved in Answer 27-3:

y=x^2 − 1

and

y=−x^2 + 1

How can we sketch an approximate graph of this system, showing the two real solutions?

Answer 28-3

We can tabulate and plot several points in both functions including the real solutions, (1,0)
and (−1,0). Table 30-2 compares some values of x, some values of the first function, and some
values of the second function. Figure 30-4 shows the curves and the solution points. On both
axes, each increment represents 1 unit.

x

y

(0,0)

Figure 30-3 Illustration for Answer 28-2. The first function

is graphed as a solid curve; the second function

is graphed as a dashed curve. The real-number

solution appears as a point where the curves

intersect. On both axes, each increment is 1 unit.