Imagine you are a young engineer working for a big defense contractor. You have

Question

Imagine you are a young engineer working for a big defense contractor. You have been
assigned to the laboratory where a new material is being tested for use in the next generation of
ballistic missiles. The goal of these tests is to characterize stress induced by vibrations. Because
of budget constraints the contractor is limited to run three experiments only. For the new material
in question, suppose you collect three measurements Mi = (xi, yi), i = 1, 2, 3, where xi denotes
deflection and yi denotes stress. A curve fit of the form y = ax2 + bx + c passing through M1,
M2, and M3, is considered to be reasonable for the range of operating conditions of the missiles.
Assuming x1, x2, and x3 are distinct, how can you be certain that the curve of the form suggested will
be unique?

Explanation / Answer

Yes, it is unique, since

y = ax^2 + bx + c

has 3 unknown coeffcients. Since you have 3 points, then a, b, c for those three points are unique. [3 variables, 3 equations produce unique solutions.]

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