Solving an Equation Graphically
When finding the to an , sometimes it can be difficult to solve the equation algebraically. In such cases, solving the equation graphically can be convenient.
To solve an equation, such as
graphically, both sides should be graphed separately. Then, the
coordinates of their should be observed.
For a more concrete example, consider the following equation.
There are three steps to follow to solve the equation by graphing.
Create Two Functions From the Given Equation
Each side of the given equation forms a .
The idea here is that the functions considered should be easy to graph. In this example, the functions created are some of their . That is, is a of and is a vertical translation of
Graph the functions in the same .
When the graphs of the functions do not intersect, the equation does not have a solution.
Identify the Coordinate of the Point(s) of Intersection
The solutions of an equation are the coordinates of any of the graphs of the functions drawn. Since the graphs of the given equation intersect at two points, the equation has two solutions.
coordinates of the points are
Solving an equation graphically does not necessarily lead to an exact answer. To verify a solution, substitute it into the given equation and check if it produces a true statement.
is an exact solution. The solution
can be verified the same way.
Since the substitution resulted in a true statement,
is also a solution of the equation. Therefore, the given equation has two solutions.
Note that if the point of intersection is not a , the exact solution may not be easy to find using this method.