Question 701259: Find a polynomial of degree ≤2 [of the form f (t) = a + bt + ct^2] whose graph goes through the points (1, p), (2, q), (3,r), where p, q, r are arbitrary constants. Does such a polynomial exist for all values of p, q, r?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find a polynomial of degree ≤2 [of the form f (t) = a + bt + ct^2] whose graph goes through the points (1, p), (2, q), (3,r), where p, q, r are arbitrary constants. Does such a polynomial exist for all values of p, q, r?
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Form: ax^2 + bx + c = y
Using (1,p) you get: a + b + c = p
Using (2,q) you get: 4a+2b + c = q
Using (3,r) you get: 9a+3b + c == r
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Solutions exist as long as the coefficient
matrix is not singular i.e, as long as the
determinant of that matrix is not zero.
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Cheers,
Stan H.
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