Question

A parabola is graphed such that the axis of symmetry is x = 3. One of the x-intercepts is (5, 0). What is the other x-intercept?

Answer 1

The axis of symmetry is the fold line that splits the parabola down the middle.

Now, since a parabola is symmetrical, every point, except the vertex, will have a mirror image of another point if we folded the parabola over the axis of symmetry.

So if we know the axis of symmetry is x = 3 and one of our points

has the coordinates (5, 0), the other point will have the coordinates (3, 0).

The axis of symmetry is always halfway between the x-intercepts.