For the general quadratic equation:
[tex]ax^2+bx+c=0[/tex]
the solutions are given by the quadractic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
The discriminant tells you how many possible solutions a particular quadratic equation has and is given by the term into the square root:
[tex]b^2-4ac[/tex]
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
[tex]ax^2+bx+c=0[/tex]
is the same as
[tex]y=0[/tex]
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
