As x= -3 is the only x-intercept of the graph of a quadratic equation.
Which means that there are equal roots of the quadratic equation.
When the roots are equal then discriminant is zero.
[tex]b^{2}-4ac = 0[/tex]
When the roots are not real then [tex]b^{2}-4ac < 0[/tex]
When the roots are real and different (unequal) then
[tex]b^{2}-4ac > 0[/tex]
As in the given question x= -3 is the only root of the quadratic equation so the discriminant is zero
