EXPLORING DATA AND STATISTICS Modeling with Polynomial ...
Page 1 of 2380Chapter 6Polynomials and Polynomial FunctionsModeling with Polynomial FunctionsUSINGFINITEDIFFERENCESYou know that two points determine a line and that three points determine a Example 1 you will see that four points determine the graph of a cubic a Cubic FunctionWrite the cubic function whose graph is shown at the the three given x-intercepts to write the following: (x) = a(x+ 3)(x 2)(x 5)To find a, substitute the coordinates of the fourth point. 15= a(0+ 3)(0 2)(0 5), so a= 21 (x) = 12 (x+ 3)(x 2)(x 5) CHECK Check the graph s end behavior. The degree of is odd and a < 0, so (x) + as x and (x) as x + .. . . . . . . . . .To decide whether y-values for equally-spaced x-values can be modeled by apolynomial function, you can use Finding Finite DifferencesThe first three triangular numbers are shown at the right. A formula for the nth triangular number is (n) = 12 (n2+ n). Show that this function has constant second-order the first several triangular numbers.
Page 1 of 2 6.9 Modeling with Polynomial Functions 381 In Example 2 notice that the function has degree two and that the second-order differences are constant. This illustrates the first property of finite differences.
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