When solving a quadratic equation you have
0,1,2 solutions. What does this mean "graphically?

If there are no real solutions, the graph does not 
cross the x axis.  It would either look like something like this:



or like this



If there is just one real solution, the graph just touches but does
not cross the x axis.  It would either look like something like this,
which has the one solution x = 1



or like this, whose one solution is x = 5



If there is just one real solution, the graph cross the x axis
twice.  It would either look like something like this, whose
two solutions are x = 2 and x = 4:



or like this, which has the two solutions x=1 and x = 5



Edwin