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-16x^2 + 144x = 288 (1) ====>
16x^2 - 144x + 288 = 0 is equivalent to
x^2 - 9x + 18 = 0
(x-3)*(x-6) = 0.
The roots of the equation (1) are 3 and 6 seconds.
So, the object is above the height of 144 ft from the time moment of 3 seconds till the time moment of 6 seconds,
or exactly 3 = 6 - 3 seconds. ANSWER
Solved.
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In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
- Problem on a ball thrown vertically up from the top of a tower
- Problem on a toy rocket launched vertically up from a tall platform
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.