Unformatted text preview: = 0 but we
know N (0) = 2.
(b) The quadratic model for the hours of daylight in Fairbanks, Alaska is y = .51x2 +6.23x −
.36. Even with R2 = .92295 we should be wary of making predictions beyond the data.
Case in point, the model gives −4.84 hours of daylight when x = 13. So January 21,
2010 will be “extra dark”? Obviously a parabola pointing down isn’t telling us the whole
story. Chapter 3 Polynomial Functions
3.1 Graphs of Polynomials Three of the families of functions studied thus far: constant, linear and quadratic, belong to a much
larger group of functions called polynomials. We begin our formal study of general polynomials
with a deﬁnition and some examples.
Definition 3.1. A polynomial function is a function of the form:
f (x) = an xn + an−1 xn−1 + . . . + a2 x2 + a1 x + a0 ,
where a0 , a1 . . . . an are real numbers and n ≥ 1 is a natural number.a The domain of a polynomial
function is (−∞, ∞).
a Recall this means n is a ‘counting number’ n = 1, 2, 3, . . . There are several things about Deﬁnition 3.1 that may be oﬀ-p...
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