X-Intercept
The x-intercept of a graph of a function f represented in a Cartesian plane is the name given to the x-coordinate of each of the points where the graph of f intersects with the
x-axis, or the point(s) of the graph for which [latex]f(x) = 0[/latex].
The expression "x-intercept" can also indicate each of the points where the line of a function intersects with the x-axis. It consists of points for which the x-coordinate is zero.
The x-coordinates of these points are also called the zeros of the function f.
Example
- A line only has one x-intercept.
- Some curves have 0, 1, 2, 3, … x-intercepts.
This second-degree polynomial function has two x-intercepts, which are when [latex] x = -8 [/latex] or x = 2. These two values are also the zeros of the function defined by [latex]f(x) = 0.5 (x + 8)(x - 2)[/latex]. These are the two points where the graph of the function crosses the x-axis.
- Theoretically, this graph has an infinite number of x-intercepts:
