You calculate the average value of the roots.
Xm = (x'+x")/2
We have too:
y = ax^2 +bx + c
Or
y = a(x-x')(x-x")
You can substitute x' and x"
An exemple with, x' = 1 and x' = 2
We could stay:
y = a(x-1)(x-2)
y = a(x.x-2x -x+2)
y = a(x^2-3x+2)
y = ax^2-3ax+2a
We can to make a = 1
y = x^2 -3x +2
When we substitute Xm here,
We will have the value from Ym
As Xm = (x'+x")/2
Then,
Xm = (1+2)/2
Xm = 3/2
Then,
Ym = (xm)^2 -3(xm)+2
Ym = (3/2)^2 -3(3/2)+2
Ym = 9/4 -9/2 +2
Souvind this:
Ym = -1/4
This mean,
(Xm, ym) = (3/2, -1/4)
