Geometric Construction 3


In this drawing, express y in terms of a and x.


Let a, b, c be given. Construct the graph of the function
(ax+b)x+c


Let a, b, c, d be given. Construct the graph of the function
((ax+b)x+c)x+d



Given k, a, b, c, d, construct the graphs of
k(x-a)(x-b),
k(x-a)(x-b)(x-c),
k(x-a)(x-b)(x-c)(x-d).


In this drawing, express y in terms of a, b, x, f(x) and g(x).


If f(x) = g(x) for x in a set S, and assume that a and b are not in S, how to construct a function h such that
f(x) = h(x) = g(x) for x in S
h(a) = f(a), h(b) = g(b)?

Given three points (x1,y1), (x2,y2), (x3,y3), construct the graph of the quadratic polynomial p satisfying
p(x1) = y1
p(x2) = y2
p(x3) = y3


Given four points (x1,y1), (x2,y2), (x3,y3), (x4,y4), construct the graph of the cubic polynomial p satisfying
p(x1) = y1
p(x2) = y2
p(x3) = y3
p(x4) = y4