The first part is to find a quadratic parametric curve f(t) = (p1(t),p2(t)) which passes through the points (0,0) (1,1) and (2,1). (hint: find two interpolating polynomials, one for x and one for y)
Second part is to find the control points for the curve( ie. change basis to the berstein basis)
The Attempt at a Solution
I'm not exactly sure what the first part wants, but I have the equation:
f(t) = ( t, -1/2*t^2 + 3/2*t )
I got the y component from using the Newton form.
For the second part, I don't know how to get the control points. I would assume the first and second given points are control points, and the middle control point is the only one to find. We have been shown that you can get another control point by find the intersection of the tangent lines of the first and last control point. However I don't know if this point will result in a curve that goes exactly through the given middle point. I would change basis to the berstein basis, but I have no idea how to do that. That is the part would like to know more about.