Need help finding intercept in a polynomial function

Hello,

I have a polynomial function and I would like to find all the "x" values for a "y" value.

For example I have tried to plot this function:

x=[0:0.05:23]

f=@(x) 152.094827571469-206.917405701416*x+188.571689289441*(x.^2)-93.85238987*(x.^3)+25.7783269818991*(x.^4)-4.34657779503011*(x.^5)+0.485315204*(x.^6)-0.0353709647924109*(x.^7)+0.00158130195601334*(x.^8)-0.0000388214150997567*(x.^9)+0.000000397986046326228*(x.^10)

y=f(x)

plot(x,y)

grid on

I have tried to do all the intercepts with the interp1 formula (for example when y=600)

x0=interp1(y,x,600,'nearest')

x1=interp1(y,x,600,'linear')

x2=interp1(y,x,600,'spline')

x3=interp1(y,x,600,'pchip')

x4=interp1(y,x,600,'cubic')

x5=interp1(y,x,600,'v5cubic')

As you can see in the graph I should get 2 points when y=600 but I only one and it is the same for all the y values I use.

Please if you know any way to find all the interceptions when y=600 or any value it would be very helpful!

Thank you for your time and help.

Answer 1

[James Tursa]

Why can't you just find the real roots of f(x)-600? What am I missing here?

[Guillaume]

Indeed, and that would be trivial to do if the polynomial was expressed as a vector of coefficients instead of being hardcoded in an anonymous function:

p = fliplr([152.094827571469;
            -206.917405701416;
            188.571689289441;
            -93.85238987;
            25.7783269818991
            -4.34657779503011
            0.485315204
            -0.0353709647924109
            0.00158130195601334
            -0.0000388214150997567
            0.000000397986046326228].')
f = @(x) polyval(p, x);
r = roots(p - [zeros(1, 10), 600]);
r(imag(r) == 0)

[Gerardo Flores Sempertegui]

Hi Guillaume, that solved my problem! Thank you!