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Geometric Construction 14

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

Given h, 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 (x_{1},y_{1}), (x_{2},y_{2}),
(x_{3},y_{3}), construct the graph of the quadratic polynomial
p satisfying
p(x_{1}) = y_{1}

p(x_{2}) = y_{2}

p(x_{3}) = y_{3}

Given four points (x_{1},y_{1}), (x_{2},y_{2}),
(x_{3},y_{3}), (x_{4},y_{4}), construct
the graph of the cubic polynomial p satisfying
p(x_{1}) = y_{1}

p(x_{2}) = y_{2}

p(x_{3}) = y_{3}

p(x_{4}) = y_{4}