Stitz-Zeager_College_Algebra_e-book

625 so the cable is 60625 feet above the bridge deck

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Unformatted text preview: tercepts, we set P (x) = 0 and solve −1.5x2 + 170x − 150 = 0. The mere thought of trying to factor the left hand side of this equation could do serious psychological damage, so we resort to the quadratic formula, Equation 2.5. Identifying a = −1.5, b = 170, and c = −150, we obtain 2.3 Quadratic Functions 145 x= = = = √ b2 − 4ac 2a −170 ± 1702 − 4(−1.5)(−150) 2(−1.5) √ −170 ± 28000 −3 √ 170 ± 20 70 3 −b ± √ √ We get two x-intercepts: 170−20 70 , 0 and 170+20 70 , 0 . To find the y -intercept, we set 3 3 x = 0 and find y = P (0) = −150 for a y -intercept of (0, −150). To find the vertex, we use the fact that P (x) = −1.5x2 + 170x − 150 is in the general form of a quadratic function and 170 appeal to Equation 2.4. Substituting a = −1.5 and b = 170, we get x = − 2(−1.5) = 170 . 3 170 14000 To find the y -coordinate of the vertex, we compute P 3 = 3 and find our vertex is 170 14000 . The axis of symmetry is the vertical line passing through the vertex so it i...
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