Geometric Constructions 3

Given Q_{1}(x_{1},y_{1}),Q_{2}(x_{2},y_{2})
and Q_{3}(x_{3},y_{3}), construct
the graph of the polynomial p(x) satisfying
p(x_{1}) = y_{1}, p(x_{2})
= y_{2}, p(x_{3}) = y_{3}.

Given (x_{1},y_{1}), (x_{2},y_{2}),
(x_{3},y_{3}) and (x_{4},y_{4}),
construct the graph of the polynomial p(x) satisfying
p(x_{1}) = y_{1}, p(x_{2})
= y_{2}, p(x_{3}) = y_{3},
p(x_{4}) = y_{4 }.
JavaSketchpad
file

Given 1, a, b, c, d, construct
the graph of the polynomial
(xa)(xb)(xc)(xd).

Given four points p_{0}, p_{1},p_{2},p_{3},
construct
the Bezier cubic curve passing through these points.

Construct
the parabola tangent to two given straight lines at two given points on
each of the lines.