This exercise relates to Figure 9(b) on page 62. That figure shows a graph of the equati...

This exercise relates to Figure 9(b) on page 62. That figure shows a graph of the equation Note that this equation is solved for x rather than y. In the standard Cartesian graphing mode, however, most graphing utilities require that the equation be solved for y. This exercise shows one method for obtaining the graph. (A remark at the end of this exercise mentions a second method.)

(a) Rewrite the equation as

Then solve for y in terms of x by using the quadratic formula with a = 1, b= -0.1, and c= -(15 + x). After simplifying, you should obtain

(b) Enter and graph the pair of equations

using the viewing rectangle [-20, 5, 5] by [-10, 10, 5]. Check that your graph agrees with that shown in Figure 9(b).

(c) Experiment to find a viewing rectangle in which it is clear that the graph of the equation x = y² - 0.1y - 15 is not symmetric about the x-axis.

Remark: Asecond method for graphing x = y² -0.1y -15 requires the parametric mode on your graphing utility. Consult the user’s manual for your graphing utility to see how to access and operate this mode. Entering the following pair of equations in the parametric mode will yield the graph (or a portion of the graph): x = t² - 0.1t - 15; y = t.