# Finding the control points of a quadratic Bézier curve

So I have a quadratic Bézier curve which starts in $(1,1)$ and ends in $(0,0)$. It starts with a slope of $1/2$ and ends with a slope of $-1$. I want to determine its control points.

So first of all, since it's quadratic, it will only have one control point. But I am not sure how to find the control point.

I have solved this problem now, the quadratic Bézier curve will be on some form $f(x) = a + bx + cx^2$, thus the derivative of the curve at the points $(1,1)$ and $(0,0)$ will be its tangents.