For the general quadratic equation:

the solutions are given by the quadractic formula
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://img.qammunity.org/2023/formulas/mathematics/college/rxvf73usjbbwyik14knxdemoz21vfz2ufc.png)
The discriminant tells you how many possible solutions a particular quadratic equation has and is given by the term into the square root:

If the discriminant is negative, the quadratic equation has no real solutions because the square root of negative numbers is not defined (yet)
The real solutions correspond to the x-intercepts of a given graph. Then, the answer is: x-intercepts. That is because the equation

is the same as

that is, the solutions are the x-values where y is equal to zero, which are the x-intercepts.
In other words, they are the locations where the function crosses or touches the x-axis