From Förberedande kurs i matematik 1

A point lies on the \displaystyle x -axis if it has \displaystyle y -coordinate \displaystyle 0 and we therefore look for all the points on the curve \displaystyle y=x^{\text{2}}-\text{1} where \displaystyle y=0, i.e. all points which satisfy the equation

\displaystyle 0=x^{\text{2}}-\text{1}

This equation has solutions \displaystyle x=\pm \text{1}, which means that the points of intersection are \displaystyle \left( -1 \right.,\left. 0 \right) and \displaystyle \left( 1 \right.,\left. 0 \right).