TITLE: Parabola always through two points.
QUESTION [7 upvotes]: I need to draw parabola through two points, but also need to be able to change the width of the parabola.
In more details let's say I have parabola:
$f ( x ) = - \frac { ( x - 1 ) ^ { 2 } } { W } + 1$
And no matter what $W$ I define I want my parabola goes through points (0,0) and (1,1) which for that case happens only if $W=1$.
I suppose I need to rotate the parabola or move whole parabola in some way. But don't know how to do that.
My aim is to increase $W$ to infinity until I get straight line (infinity almost straight)  through mentioned points. And in the future of course I want to be able to manipulate those points.
For any help thanks in advance.

REPLY [4 votes]: I think
$$
f(x) = \frac{x(x-1)}{W} + x
$$
will do what you want.
For large $W$ this will be nearly straight between the two points you specified. For very large $x$ (positive or negative) it will grow without bound.
(This is what happens if you finish the algebra that @KKZiomek started.)