Question

If a parabola has x-intercepts at (−7, 0) and (7, 0), which of these points could possibly be its vertex?

(0, 12)

(14, 7)

(−14, −10)

(3, 16)

Answer 1

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:

1. \((0, 12)\) - This point has an x-coordinate of 0, which is consistent with the vertex's expected x-coordinate.
2. \((14, 7)\) - This point does not have an x-coordinate of 0.
3. \((-14, -10)\) - This point does not have an x-coordinate of 0.
4. \((3, 16)\) - 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:

\((0, 12)\)