Generally you need to have as many points as you have variables. It looks like we have three simple points to work with: A(0, 1), B(0.4, 2), and C(0.9, -1). You are likely going to need one more. I'd start with point A...The exponential term in the front can't be zero so that means the sum of your trig functions would be 0.
Give it a try and get back to us.
Addendum: You might have a zero: D(0.65, 0)
period close to 0.33 =1/3 ... $\implies \beta = 6\pi$
$f(0)=1 \implies B=1$
$f(0.15) = 0 \implies A \approx 3.07$
tweaked the exponent power coefficient $\alpha = -1.2$
not a bad fit, check the attached graph in the same window ... you can tweak it some more if you want.