How to move the control points of the cubic Bézier curve, to keep the curve invariant?

Question

I have 3 cubic Bézier curves with different control points:

1. https://cubic-bezier.com/#.17,.8,.77,1
2. https://cubic-bezier.com/#.18,.59,.5,1
3. https://cubic-bezier.com/#.12,.41,.41,1

They look similar to each other. Assuming the anchor points $P_0=(0, 0)$, $P_3=(1, 1)$ are static, Is there a way to move $P_1$, $P_2$ while keeping the curve invariant?

Answer 1

A cubic Bezier curve is defined by the 4 control points. Any change to any control point will result in a different curve. So, moving $P_1$ or $P_2$ while keeping $P_0$ and $P_3$ unchanged will still change the curve.