document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108742>Question 1108742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a test next week and need help working out and solving <BR>\n" );
document.write( "a problem. If you could please help me with the steps that would be great!<BR>\n" );
document.write( "James Bond stands on top of a 240-foot building and throws a film canister<BR>\n" );
document.write( "upward to a fellow agent in a helicopter 16ft above the building. The height<BR>\n" );
document.write( "of the film canister above the ground t seconds later given by the formula<BR>\n" );
document.write( "H(t) = -16t^2 +32t + 240, where is h is in feet?\r<BR>\n" );
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document.write( "A.    If the film canister reaches the agent in the helicopter at its<BR>\n" );
document.write( "highest point, how long will it take the film canister to reach the agent?\r<BR>\n" );
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document.write( "B.    If the film canister is not caught by the agent in the helicopter and<BR>\n" );
document.write( "falls to the ground, how long will it take to hit the ground? Solve by<BR>\n" );
document.write( "factoring. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723751 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Sure. I will do it in two steps.\r<BR>\n" );
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document.write( "At the first step, I send you the list of my lessons in this site related to similar problems.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-projectile-moving-vertically.lesson>Problem on a projectile moving vertically up and down</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-projectile-shooted-vertically-upward.lesson>Problem on an arrow shot vertically upward</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-problems-on-an-projectile-moving-vertically-up-and-down.lesson>Problem on a ball thrown vertically up from the top of a tower</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-toy-rocket-launched-vertically-up--from-the-top-of-a-platform.lesson>Problem on a toy rocket launched vertically up from a tall platform</A>\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this textbook under the topic \"<U>Projectiles launched/thrown and moving vertically up and dawn</U>\".\r<BR>\n" );
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document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-I<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( "========================\r<BR>\n" );
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document.write( "At the second step, I will show you how to solve your problem.\r<BR>\n" );
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document.write( "A. If the film canister reaches the agent in the helicopter at its highest point, how long will it take the film canister to reach the agent? \r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    The question is: for how long the canister will reach its highest point ?\r\n" );
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document.write( "    It is about at what value of \"t\" the quadratic form H(t) =  -16t^2 +32t + 240  will reach its maximum ?\r\n" );
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document.write( "    From the general theory, it will happen at t = \" <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \", refering to the general form  q(x) = ax^2 + bx + c.\r\n" );
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document.write( "    In your case it will happen at t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32%2F%282%2A%28-16%29%29 ALIGN=MIDDLE  ALT=\"-32%2F%282%2A%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 second.\r\n" );
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document.write( "    So, question A is just answered.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "B. If the film canister is not caught by the agent in the helicopter and falls to the ground, how long will it take to hit the ground? Solve by factoring\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"> \r\n" );
document.write( "    This event will happen when H(t) = 0,  which is\r\n" );
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document.write( "    -16^t^2 + 32t + 240 = 0.\r\n" );
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document.write( "    As they ask us, I will solve this quadratic equation by factoring the left side polynomial\r\n" );
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document.write( "    -16(t-5)*(t+3) = 0.\r\n" );
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document.write( "    It gives you the UNIQUE positive root t= 5, which means that the canister will reach the ground in 5 seconds after it was thrown upward.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "The addition portion of the lessons on finding the maximum/minimum of a quadratic function is this:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>\r<BR>\n" );
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document.write( "Again, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this textbook under the topic \"<U>Finding minimum/maximum of quadratic functions</U>\". \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Free of charge online textbook in ALGEBRA-I<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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