# What is the difference between x-intercepts, zeros, and roots?

Zeros and roots are the same. An $x$-intercept is a point on a graph $y = f \left(x\right)$ where $x$ is a root of $f$.
Given a function $f$, a zero or root of $f$ is a value ${x}_{0}$ at which $f \left({x}_{0}\right) = 0$. If we graph the equation $y = f \left(x\right)$ on a cartesian plane, then the $x$-intercepts are the points at which $y = 0$, meaning they occur exactly where $f \left(x\right) = 0$, i.e. where $x$ is a root of the function.