# Thread: Need help creating an expression/function for a specific curve

1. ## Need help creating an expression/function for a specific curve

Hello everyone. I'm not sure if this question falls more into the algebra side of things or the trig side of things, but I figured this would be a good place to start.

Here's the problem. I need to find a function for a curve where f(x) = 0 when x = 0 or x = 1.

Now, the obvious solution is f(x) = sin(x * pi)

Here is the problem, a sin curve is too gradual. I need the curve to be close to its peak from....lets say x = .2 to x = .8, arbitrarily speaking.

I've tried taking a basic parabola, reflecting it across the x axis, and trying to adjust it's parameters to make a functional curve, but it hasn't gone so well.

Can any one educate me on creating this function, or maybe if its easier can I simply change the slope of the sin curve? (I don't think I can, but it's worth asking)

2. Hi

If I have well understood you can select $\displaystyle f(x) = x^a(1-x)^b$ where a and b are parameters

The lower values you chose for a and b, the "flatter" the curve is
You can take for instance a=b=0.1

3. Originally Posted by running-gag
Hi

If I have well understood you can select $\displaystyle f(x) = x^a(1-x)^b$ where a and b are parameters

The lower values you chose for a and b, the "flatter" the curve is
You can take for instance a=b=0.1
Thank you, that is exactly what I needed. Perhaps I would've noticed if I had remembered to factor $\displaystyle x^2$ into x * x, but it's been a while.