Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 9 - Quadratic Functions and Equations - 9-2 Quadratic Functions - Practice and Problem-Solving Exercises - Page 545: 34


(For this question, units are in feet) It's basically a graphing question - the x-axis represents the surface of the water - the shape of the graph is the same as the shape of the arch First, find out x-interception (y=0) when y=0 -0.628x^{2}+4.5x=0 x(-0.628x+4.5)=0 x=0 or -0.628x+4.5=0 -0.628x=-4.5 x=\frac{-4.5}{-0.628} x=7.17 therefore x-intercept (0,0) and (7.17,0)

Work Step by Step

Second, find the turning point the x corrdinate of the turning point is the midpoint of the x-intercept therefore $(0+7.17)\div2=3.56$ x=3.56 sub x=3.56 into the equation $y=(-0.628)\times3.56x^{2}+4.5\times3.56$ y=8.06 therefore the turning point is (3.56, 8.06) So, when the water level rises by 5.5 feet $5.5\lt8.06$ therefore, the top of the arch support is above the water
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