y = x^2 - 4x - 32 axis of symmetry = 2      vertex = (2,-36) x-intercepts = (-4,0) (8,0) How dose the axis of symmetry relate to the x-intercepts?

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justaguide eNotes educator| Certified Educator

The equation of the parabola is: y = x^2 - 4x - 32

The axis of symmetry is x = 2. The x-intercepts are (-4,0) and (8,0).

The distance of the x-intercepts from the axis of symmetry is the same, here it is 6 units. This is the case as the axis of symmetry is a line that splits the graph in two such that each side is a mirror image of the other side.

As a result, the distance of (-4,0) from x = 2 is the same as that of the point (8,0) from x = 2.