Almost any equation in
one variable can be solved graphically. The strategy is as follows:
graph the left hand side and the right hand side of the equation on
the same coordinate axes, and then trace the graph to find the point(s)
where the two curves intersect. If there is no point of intersection
then we say that the equation has no solution. The following example
will illustrate this procedure.
Find all solutions of the
equation . Round your answers to three decimal places.
First we will use the Plot-Solve
tool to graph the left-hand side of the equation, and the right-hand side, on the same coordinate axes. See Figure 1.
The graph shows that there
are two points of intersection. Click on one of the points and zoom
in to find the coordinates of that point of intersection. Figure 2
shows that the intersection point on the left has coordinates (-3.3,
We can repeat the process
to find the right intersection point. The coordinates are
(45.2, 60). See Figure
The equation has two solutions,
to one decimal place.