You can put this solution on YOUR website! No.
Simple example, , only one intercept with x-axis.
Different parabola, , moved upward by 1/8 units and y will not touch the x-axis anywhere.
You can put this solution on YOUR website! No for many reasons.
If the parabola opens on the right side or left side it will only cross the x axis at most once
The parabola might have its vertex on the x axis
The vertex might be above or below the x axis and so might not cross the x axis at all.