Question 62566
<pre>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:

{{{ graph( 200, 200, -3, 7, -5, 5, (x-4)^2-(x-4)+2) }}}

or like this

{{{ graph( 200, 200, -3, 7, -5, 5, -(x-2)^2+(x-2)-2) }}}

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

{{{ graph( 200, 200, -3, 7, -5, 5, (x-1)^2) }}}

or like this, whose one solution is x = 5

{{{ graph( 200, 200, -3, 7, -5, 5, -(x-5)^2) }}}

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:

{{{ graph( 200, 200, -3, 7, -5, 5, (x-2)(x-4)) }}}

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

{{{ graph( 200, 200, -3, 7, -5, 5, -x^2+6x-5) }}}

Edwin</pre>