NP. Its worth having a simple example in your pocket so say you had a quadratic
y = ax^2 + bx + c
intersecting a horizontal line
y = d
The sum of the roots of the original quadratic is -b/a (twice the stationary point -b/2a), which you can think about algebraically as the quadratic is
or by noting that the quadratic formula gives
x = -b/2a +/-....
When you add the two roots, the ... cancels and r1+r2 = -b/a, so twice the stationary point or twice the average of the roots.
This holds for the sum of the intersection points as the quadratic is unchanged apart from the constant becomes c-d, so the average (sum) of the roots does not change its -b/2a. Its independent of the value of the constant c.