How Do Different t Values Affect a Bezier Curve?

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Homework Statement


I am working on an investigation about bezier curve. Given 4 points (starting point, ending point and two different control points). 0.2 was my given t value. One of the tasks was using different value of a parameter t such as 0.3, 0.5, 0.75 and 0.9. I was asked to explain the anomalies and the significance of those value of t. But I don't quite know how to explain and what I really should be looking for, can anyone please give me some suggestions?

Homework Equations





The Attempt at a Solution


After finding different points of P, I connected them and formed a curve. I reckon the curve is the resultant curve.
 
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Hi! If you haven't looked yet, this Wikipedia article section is a lot of help.

As for your questions, could you perhaps provide a little more information?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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