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?
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.