Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.8 Use the Quadratic Formula and the Discriminant - Guided Practice for Example 5 - Page 295: 10


The ball will be in the air for about $3.14$ seconds.

Work Step by Step

Write height model. $h=-16t^{2}+v_{0}t+h_{0} \qquad$ ...substitute $3$ for $h, 50$ for $v_{0},$ and $4$ for $h_{0}$ . $ 3=-16t^{2}+50t+4\qquad$ ...add $-3$ to each side. $ 3-3=-16t^{2}+50t+4-3\qquad$...simplify. $ 0=-16t^{2}+50t+1\qquad$ ...write in standard form. $ 16t^{2}-50t-1=0\qquad$ ...use the Quadratic formula: $x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ $ t=\displaystyle \frac{-(-50)\pm\sqrt{(-50)^{2}-4(16)(-1)}}{2(16)}\qquad$...simplify. $ t=\displaystyle \frac{50\pm\sqrt{2564}}{32}\qquad$...simplify. ...since we are calculating time, we can discard the negative solution. $ t=\displaystyle \frac{25+\sqrt{641}}{16}\qquad$...use calculator $t\approx 3.14$.
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