Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a

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Suppose Experimental Data Are Represented By A Set Of Points In The Plane An Interpolating Polynomial For The Data Is A 1 (46.05 KiB) Viewed 59 times

Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t) = a + a₁ + a₂t² for the data (1,10), (2,14), (3,20). That is, find a, a₁, and a2 such that the following is true. ª。 +â₁ (1) + a₂ (1)² = = 10 a₁ + a₁ (2) + a₂ (2)² = = 14 a₁ + a₁ (3) + a₂ (3)² = = 20