Intercepts calculator

One of the tasks which arises in function analysis is finding the intersection points of the function with coordinate axes. Consider the algorithm of solving this task on concrete example. For simplicity, we'll work with single variable function:

The graph of this function is presented on the figure:

From the figure it follows that our function intersects axis in two points and axis in one point.

At first we'll find the intersection points of function with axis. Notice, that in these points . That's why to find them, we need to solve the equation:

This quadratic equation has two roots:

Thus, we have found two intersection points of our function with abscissa axis: and . It should be noted that the task of finding intersections of function with axis is equivalent to the task of finding function's zeros.

Now, let's find the intersection point with ordinate axis. In this point the coordinate . So, to find them, we simply put the value into our function:

So, we have found the intersection point of our function with ordinate axis .