Question

Which pair of points could the parabola intersect the X-axis if the equation of the axis of symmetry is X = 2?

A) (0, 0) and (4, 0)
B) (1, 0) and (3, 0)
C) (-2, 0) and (6, 0)
D) (-3, 0) and (7, 0)

Please choose the correct option.

Answer 1

The correct answer is B) (1, 0) and (3, 0) because these points are equidistant from the axis of symmetry X = 2, which is a necessary condition for points where a parabola intersects the X-axis.

Step-by-step explanation:

The question is asking for the points at which a parabola intersects the X-axis given that the equation of the axis of symmetry is X = 2. The axis of symmetry for a parabola runs parallel to the Y-axis and divides the parabola into two mirrored halves. If the axis of symmetry is X = 2, then the parabola will intersect the X-axis at points that are equidistant from X = 2.

The correct answer is B) (1, 0) and (3, 0) because these points are both 1 unit away from the line of symmetry, X = 2. Options A), C), and D) do not have points that are symmetrically placed around X = 2.