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Stitz-Zeager_College_Algebra_e-book

50 if we sell 57 game systems 5 in the previous part

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Unformatted text preview: get g (x) = 0 −2(x − 3)2 + 1 = 0 −2(x − 3)2 = −1 1 (x − 3)2 = 2 divide by −2 1 √2 2 x−3 = ± 2√ extract square roots x−3 = ± rationalize the denominator 2 2 √ 6± 2 2 x = 3± x= get a common denominator √ √ Hence, we have two x-intercepts: 6+2 2 , 0 and 6−2 2 , 0 . (The inquisitive reader may wonder what we would have done had we chosen to set the expanded form of g (x) equal to zero. Since −2x2 + 12x − 17 does not factor nicely, we would have had to resort to other methods, which are reviewed later in this section, to solve −2x2 + 12x − 17 = 0.) To ﬁnd the y -intercept, we set x = 0 and get g (0) = −17. Our y -intercept is then (0, −17). Plotting some additional points, we get y 1 −1 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11 −12 −13 −14 −15 −16 −17 1 2 3 4 5 x g (x) = −2(x − 3)2 + 1 2.3 Quadratic Functions 141 The domain of g is (−∞, ∞) and the range is (−∞, 1]. The function g is increasing on (−...
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