Stitz-Zeager_College_Algebra_e-book

If we consider f x x2 x 6 and g x 0 then solving

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Unformatted text preview: what shape a free hanging cable makes. 150 2.3.2 Linear and Quadratic Functions Answers 1. (a) f (x) = x2 + 2 No x-intercepts y -intercept (0, 2) Domain: (−∞, ∞) Range: [2, ∞) Decreasing on (−∞, 0] Increasing on [0, ∞) Vertex (0, 2) is a minimum Axis of symmetry x = 0 (b) f (x) = −(x + 2)2 x-intercept (−2, 0) y -intercept (0, −4) Domain: (−∞, ∞) Range: (−∞, 0] Increasing on (−∞, −2] Decreasing on [−2, ∞) Vertex (−2, 0) is a maximum Axis of symmetry x = −2 (c) f (x) = x2 − 2x − 8 = (x − 1)2 − 9 x-intercepts (−2, 0) and (4, 0) y -intercept (0, −8) Domain: (−∞, ∞) Range: [−9, ∞) Decreasing on (−∞, 1] Increasing on [1, ∞) Vertex (1, −9) is a minimum Axis of symmetry x = 1 (d) f (x) = −2(x + 1)2 √ 4 + √ x-intercepts (−1 − 2, 0) and (−1 + 2, 0) y -intercept (0, 2) Domain: (−∞, ∞) Range: (−∞, 4]) Increasing on (−∞, −1] Decreasing on [−1, ∞) Vertex (−1, 4) is a maximum Axis of symmetry x = −1 y 10 9 8 7 6 5 4 3 2 1 −2 −1 1 x 2 y x −4 −3 −2 −1 −1 −2...
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