How can I find the intersection from two fitting line?

I have two fitting models as below:

Linear model:
     f(x) = a*(sin(x-pi)) + b*((x-10)^2) + c
     Coefficients (with 95% confidence bounds):
       a =       1.827  (-0.4519, 4.106)
       b =     -0.1606  (-0.2539, -0.06737)
       c =       22.76  (17.64, 27.88)

And

Linear model Poly3:
     g(x) = p1*x^3 + p2*x^2 + p3*x + p4
     Coefficients (with 95% confidence bounds):
       p1 =       24.22  (21.22, 27.23)
       p2 =      -305.6  (-342.3, -268.8)
       p3 =        1287  (1137, 1437)
       p4 =       -1793  (-1996, -1589)

How can I find the intersections of these models(x is between 3:4)?

Answer 1

[Star Strider]

First, plot the two functions. That reveals only one intersection. Then create anonymous functions from them, and a third anonymous function that subtracts them, and use fzero to find the zero-crossing. This gives you the intersection at 4.7157.

The Code:

a =       1.827;
b =     -0.1606;
c =       22.76;
f = @(x) a*(sin(x-pi)) + b*((x-10).^2) + c;

p1 =       24.22;
p2 =      -305.6;
p3 =        1287;
p4 =       -1793;
g = @(x) p1*x.^3 + p2*x.^2 + p3*x + p4;

fg = @(x) f(x) - g(x);
xint = fzero(fg, 1)

x = linspace(4, 5);

figure(1)
plot(x, fg(x))
hold on
plot(xint, 0, 'pr', 'MarkerFaceColor','g')
hold off
grid

figure(2)
plot(x, f(x))
hold on
plot(x, g(x))
plot(xint, f(xint),  'pr', 'MarkerFaceColor','g')
hold off
grid

xint =
     4.7157

Answer 2

[KSSV]

Have a look on this file exchange:

https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections