Algebra 1 8th Grade
posted by Nancy .
What is the relationship between the
xintercepts of a parabola and its vertex's xcoordinate?

if you average the xintercepts , you get the x coordinate of the vertex.
y = x^2  2x  8
= (x4)(x+2)
so the x intercepts are 4 and 2
average of those = (2 + 4)/2 = 1
so the vertex is (1, ...) 
If I were to write down:
"When you find the median between the two intercepts, it is the xintercept of the vertex."
do you think that's a true relationship still ? 
I would use the word "mean"
"Mean" is what is known as the average in everyday language, "median" is the middle value of a set of data.
Of course if you only have two data values, as the xintercepts, it actually does not matter.