Since the solutions of the equations give the x-intercepts of the graphs, the number of x-intercepts is the same as the number of solutions. The point on the parabola that is on the axis of symmetry i...Since the solutions of the equations give the x-intercepts of the graphs, the number of x-intercepts is the same as the number of solutions. The point on the parabola that is on the axis of symmetry is called the vertex of the parabola; it is the lowest or highest point on the parabola, depending on whether the parabola opens upwards or downwards.