Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 9 - Quadratic Functions and Equations - 9-2 Quadratic Functions - Practice and Problem-Solving Exercises: 30

Answer

$\approx$74.3 feet

Work Step by Step

To find the height of the geyser at any time, we will use the equation: $s= ut+(1/2)at^2$ Next, we simply plug in our given variables. $h= 69t +(1/2)(-32.174)t^2$ This then simplifies to: $h =69t - 16.09t^2$ This formula represents a quadratic formula that will have a maximum value. Use the axis of symmetry formula, -b/2a, and plug in the variables accordingly. $$ 69/2(16.09) \\ \approx2.14$$ Plug this value in for t to find h in the quadratic equation. $$h =69(2.14)-16.09(2.14)^2 \\ \approx 74.3$$
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