The x-intercepts of the parabola are given at the points \((-7, 0)\) and \((7, 0)\). This indicates that the parabola is symmetric about the y-axis, and the x-coordinate of the vertex must be 0 (the midpoint of the x-intercepts).
The vertex of the parabola will be located directly above or below the midpoint of the x-intercepts, which is at \((0, k)\), where \(k\) is some real number.
Among the options given for possible vertex points:
- \((0, 12)\) - This point has an x-coordinate of 0, which is consistent with the vertex's expected x-coordinate.
- \((14, 7)\) - This point does not have an x-coordinate of 0.
- \((-14, -10)\) - This point does not have an x-coordinate of 0.
- \((3, 16)\) - This point does not have an x-coordinate of 0.
Since the only point with an x-coordinate of 0 is \((0, 12)\), that is the only possible vertex of the parabola.
Thus, the answer is:
\((0, 12)\)