Question 36342
When the descriminant is positive, the parabola is either like a U with the vertex below the x-axis, or like an upside-down U with the vertex above the x-axis (so either way, the parabola intersects the x-axis at 2 points).  When the descriminant is 0, the vertex is on the x-axis (like y=x^2), and when the descriminant is negative it never touches the x-axis.  So it either starts above and continues up or starts below and continues down (like y=x^2+3 or y=-x^2-3).
I believe that's part of what the question is looking for.