## How to stop a parabola from intersecting itself?

Asked by Jasmine Alvarez

### Jasmine Alvarez (view profile)

on 2 Mar 2018
Latest activity Edited by Jan

### Jan (view profile)

on 2 Mar 2018
Accepted Answer by Jan

### Jan (view profile)

I need to graph multiple parabolas on one plot, but when I plot the entire parabola (symmetric across the y-axis) it intersects itself.
clc;clear;close;
RPM_v = [0.1,0.2,0.3,0.4,0.5];
R = .05;
h0 = .15;
%define constants and change units
omega_v = RPM_v.*2*pi/60; %[rad/s]
g = 9.807; %[m/s^2]
r = linspace(0,R); %[m]
phi = linspace(0,2*pi); %[rad]
r_R = r./R;
%PLOT
%2D figure
Fig_2 = figure('Name','Graphical Display with Ratio Measurements',...
'Units','normalized','Position',[.005,.005,.4,.5]);
Axes_2 = axes('Parent', Fig_2,'NextPlot', 'add');
z_v = 1;
n = 1;
while length(z_v) ~= 6
%equation of surface
z_z0 = (h0 - omega_v(n)^2/(2*g)*(R^2/2 - r.^2))/h0 %[m]
xlabel('r/R');
ylabel('z/z0');
title('RPM on a Height vs. Radius Graph');
plot(Axes_2,[-r_R,r_R],[z_z0,z_z0]);
z_v(n+1) = 1;
n = n+1;
end
RPM_num = {'RPM = 0.1','RPM = 0.2','RPM = 0.3','RPM = 0.4',...
'RPM = 0.5'};
legend(Axes_2,RPM_num);
When I just use
plot(Axes_2,r_R,z_z0);
it doesn't graph both sides of the graph. I do not know how to modify this so it displays like a normal parabola.

on 2 Mar 2018
Edited by Jan

### Jan (view profile)

on 2 Mar 2018

Replace:
plot(Axes_2,[-r_R,r_R],[z_z0,z_z0]);
by:
x = [-(r_R(end:-1:2), r_R];
y = [z_z0(end:-1:2), z_z0];
plot(Axes_2, x, y);
Your original x values are e.g. (simplified:)
r_R = [0, 1, 2]
z_z0 = [0, 1, 4]
Then you have plotted:
plot([-0,-1,-2,0,1,2], [0,1,4,0,1,4])
and this draws the unwanted line. My suggestion creates:
plot([-2,-1,0,1,2], [4,1,0,1,4])