SOLUTION: If a parabola is facing up on a graph it has a positive discriminant. Is that correct?

You can put this solution on YOUR website!
Not necessarily. It depends on whether it does
or does not intersect the x-axis.
If it crosses it at two points it will have a positive discriminant.
If it does not cross it at all it will have a negative discriminant.
If it touches it at one point it will have a zero discriminant.
Cheers,
Stan H.