Graphical solutions

You must be able to solve any equation of a single variable. For two functions $y_1(x)$ and $y_2(x)$, you must be able to say which values of $x$ solve $y_1(x)=y_2(x)$. Many equations of this form can be solved by simple algebra. For instance, the equation $x^2 + x -2 =0$ can be solved by using the quadratic equation. Sometimes, however, no simple expression can be found for the solution and the equations must be solved numerically. For instance, $3x^3-2\sin x =0$ must be solved numerically.

There are a variety of techniques to solve such equations numerically but a relatively simple and robust method is to find the solutions graphically. To find the solutions graphically, plot both sides of the equation $y_1(x)=y_2(x)$; the solutions are the points where the two graphs intersect. By zooming in to the intersection, the solutions can be determined with reasonable accuracy.

Below is a plotting program that can be used to solve an equation graphically.

In this course, a blue border will indicate that the input should be a mathematical expression that may include a variable. A black border indicates that the input should be a number. Press the button to see which mathematical functions can be used in a mathematical expression. Press the button to hide the help text.