SOLUTION: A ball is thrown straight up from a rooftop 432 feet high. The formula below describes the​ ball's height above the​ ground, h, in​ feet, t seconds after it was thrown. The b

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A ball is thrown straight up from a rooftop 432 feet high. The formula below describes the​ ball's height above the​ ground, h, in​ feet, t seconds after it was thrown. The b      Log On


   

Question 1178634: A ball is thrown straight up from a rooftop 432 feet high. The formula below describes the​ ball's height above the​ ground, h, in​ feet, t seconds after it was thrown. The ball misses the rooftop on its way down. The graph of the formula is shown. Determine when the​ ball's height will be 378 feet and identify the solution as a point on the graph.
h=-16t^2+30t+432

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
h=378
378=-16t%5E2%2B30t%2B432
0=-16t%5E2%2B30t%2B432-378
0=-16t%5E2%2B30t%2B54
0+=+-2+%28t+-+3%29+%288+t+%2B+9%29
solutions:
t=3
t=-9%2F8->throw out the negative solution
The ball will be at a height of 378 feet after 3 seconds.



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

To solve the problem and to get the answer, you need to solve this quadratic equation


    -16t^2 + 30t + 432 = 378.


Rewrite it in this equivalent form


    16t^2 - 30t - 54 = 0


Find the roots using the quadratic formula


    t = 30+%2B-+sqrt%2830%5E2+%2B+4%2A16%2A54%29%29%2F%282%2A16%29 = %2830+%2B-+sqrt%284356%29%29%2F32 = %2830+%2B-+66%29%2F32.


Only positive root  t = %2830%2B66%29%2F32 = 96%2F32 = 3 seconds is the solution to the problem.

Solved,  answered,  explained and completed.

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In this site,  there is a bunch of lessons on a projectile thrown/shot/launched vertically up
    - Introductory lesson 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

Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.
Read them attentively and learn how to solve this type of problems once and for all.

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.