If a parabola has two x-intercepts, then its vertex...

is somewhere in between the x-intercepts.

is below the x-intercepts.

is EXACTLY halfway between the x-intercepts.

is above the x-intercepts.

1 answer

If a parabola has two x-intercepts, its vertex is indeed located somewhere in between the x-intercepts. In particular, it is exactly halfway between the two x-intercepts, but it can be above or below the x-axis depending on the orientation and the position of the parabola.

  • If the parabola opens upwards, the vertex will be below the x-axis if the parabola intersects the x-axis at two points that are above the x-axis.
  • If the parabola opens downwards, the vertex will be above the x-axis if the parabola intersects the x-axis at two points that are below the x-axis.

Thus, the most appropriate answer to the question is:

is EXACTLY halfway between the x-intercepts.

This is correct for the x-coordinate of the vertex, regardless of whether it is above or below the x-axis.