Points of intersection of $n$ parabolas This is a question that just popped in my friend's mind today:

There are $n$ parabolas in a plane. What are the maximum and minimum points of intersection possible?
We have to assume that all parabolas are distinct. Also all parabolas are identical in size i.e. their length of latus rectum is same.

I thought the minimum number of points of intersections will be $n$. We can achieve this by arranging the vertices of all parabolas on a circle of large radius and then we can see that two adjacent parabolas will intersect. But this method fails for $n = 1, 2, 3, 4$ because we can have $4$ parabolas with no intersections.
How would I go about approaching this problem?
Edit:
With the help of MarkBennet in the comments, I have realised we can easily make the points of intersection to be $0$. This can be done by simply putting the next parabola translated along the axis of previous parabola.
 A: $\color{brown}{\textbf{Used parabolas.}}$
If equation of the parabola in cartesian coordinates is
$$y=x^2+R,$$
then in polar coordinates $\;x=r\cos t,y=r\sin t\;$ it takes the form of
$$r^2\cos^2 t - r\sin t +R =0,$$
with the discriminant
$\;D=\sin^2 t - 4R\cos^2 t = 1-(4R+1)\cos^2 t,\;$
which should be positive.
Therefore, the considered parabola can be inscribed in a sector of an unlimited circle with the polar angles
$$t\in\frac\pi2\pm\arcsin\frac{1}{\sqrt{4R+1}} \subset \frac\pi2\pm \arctan\frac1{\sqrt{4R}},$$
wherein the central angle of the sector is
$$\Delta t(R) = 2\arctan\frac1{2\sqrt{R}}\;\underset{R\to \infty}{-\!-\!\!\!\to}\; 0,$$
so it can be made infinitely small.
This feature can be illustrated by the WA plot.

$\color{brown}{\textbf{Placing.}}$

Placing of the possible solutions is shown on the pictures above, wherein each colored triangle correspond to the starting (empty) segment of the unlimited sector.
Left picture illustrates the placing of parabolas without intersections.
Right picture  illustrates the placing of parabolas where each pair of parabolas has four points of intersection.
Since each parabola can be inscribed in a sector of the unlimitd circle with the arbitrary small central angle, then

*

*the least number of the pairwise intersections of $\;n\;$ parabolas is $\;\color{brown}{\textbf{zero}},$ and

*the highest number of the pairwise intersections of $\;n\;$ parabolas is $\;\color{brown}{\mathbf{2n(n-1)}}.$
In particular, for $\;n=3, R=25\;$ we have $2\cdot3\cdot(3-1)= 12$ intersections
(see also WA plot).

