What is the equation to produce this Bezier curve? What is the equation for the first curve in the image?

I have this formula:

But when I substitute values, I get an image that looks like x^2.  It isn't the same shape as the image.

In the image, the curve seems to be the envelope of the lines whose $x$ and $y$ intercepts add to $1$. These lines are given by
$$
y=y_0\left(1-\frac x{1-y_0}\right)\;,
$$
where $y_0$ is the $y$ intercept.
The envelope maximizes $y$ with respect to $y_0$ for given $x$. Setting the derivative of $y$ with respect to $y_0$ to zero yields
$$
1-\frac x{1-y_0}-\frac{y_0x}{(1-y_0)^2}=0
$$
and thus $y_0=1-\sqrt x$. Substituting this into the equation for the lines yields $y=\left(1-\sqrt x\right)^2$, or in more manifestly symmetric form,
$$
\sqrt x+\sqrt y=1\;.
$$
This can also be written parametrically as $(x,y)=(\sin^4 t,\cos^4 t)$.
