document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978501>Question 978501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help on what the steps are to solve this quadratic problem. Please show the problem with steps included. Thank you :)\r<BR>\n" );
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document.write( "Imagine yourself standing on the roof of a 1450-foot Tower. When you throw a ball upward from the roof of the tower, the ball’s height above the ground, H (in feet), can be described as a function of the time, t (in seconds), since the ball was dropped.  This height function is defined by <BR>\n" );
document.write( "H(t) = -16t2 + 80t +1450\r<BR>\n" );
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document.write( "Identify the vertical intercept and  what does it mean in the context of the problem\r<BR>\n" );
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document.write( "After the baseball is thrown, how long will it take till the ball hits the ground?\r<BR>\n" );
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document.write( "Your answer to question #2 identifies one horizontal intercept of the equation.  Identify another horizontal intercept and discuss whether it makes sense in the context of the problem.\r<BR>\n" );
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document.write( "At what time(s) is the ball 1500 feet above the ground?\r<BR>\n" );
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document.write( "Identify the practical domain and range.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599879 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=599879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ball is not dropped.  The ball must be thrown UPWARD. Note the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient on x^2.  H is concave downward and H has a vertex at a maximum.\r<BR>\n" );
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document.write( "Here is a way, not the only, to find vertex.<BR>\n" );
document.write( "Roots...<BR>\n" );
document.write( "H=0,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-80%2B-+sqrt%2880%5E2-4%28-16%291450%29%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t=%28-80%2B-+sqrt%2880%5E2-4%28-16%291450%29%29%2F2%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-80%2B-+sqrt%2815360%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-80%2B-+sqrt%2815360%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "15360=6*256=6*4*64=2*3*2*2*2^6=2^9*3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-80%2B-+16sqrt%286%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-80%2B-+16sqrt%286%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%2880%2B-+16%2Asqrt%286%29%29%2F32 ALIGN=MIDDLE  ALT=\"t=%2880%2B-+16%2Asqrt%286%29%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=40%2F16%2B-+%281%2F2%29sqrt%286%29 ALIGN=MIDDLE  ALT=\"t=40%2F16%2B-+%281%2F2%29sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "t at the vertex will be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F16=20%2F8=10%2F4=5%2F2 ALIGN=MIDDLE  ALT=\"40%2F16=20%2F8=10%2F4=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is exactly in the middle of the two roots.  That is two and one-half seconds.  Use this value of t=5/2  to find  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%282.5%29 ALIGN=MIDDLE  ALT=\"H%282.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That is maximum value, the vertex of H. </SPAN>\n" );
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