document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158667>Question 1158667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem: A ball is thrown vertically upward into the air.  If the ball started from a height of 101 feet off the ground, use the following formula to represent the projection of the ball\r<BR>\n" );
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document.write( "            H=-16t^2+38t+101\r<BR>\n" );
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document.write( "where H is the height of the ball after t seconds have passed. Based on this information, answer the following questions.<BR>\n" );
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document.write( "1)When does the ball reach its maximum height?<BR>\n" );
document.write( "Your answer must be expressed as a decimal rounded to 2 decimal places with correct units. Hint: The maximum occurs at the vertex of the parabola.<BR>\n" );
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document.write( "2)What is the maximum height of the ball?<BR>\n" );
document.write( "Your answer must be expressed as a decimal rounded to 2 decimal places with correct units.<BR>\n" );
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document.write( "3)When does the ball return to the ground? <BR>\n" );
document.write( "You must use the quadratic formula to solve this problem. Your answer must be expressed as a decimal rounded to 2 decimal places with correct units.<BR>\n" );
document.write( "Hint: The ball reaches the ground when the height equals zero.  <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 #781627 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=-16t%5E2%2B38t%2B101 ALIGN=MIDDLE  ALT=\"H=-16t%5E2%2B38t%2B101\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1) maximum\r<BR>\n" );
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document.write( "you have a parabola, upside down, and max is at vertex\r<BR>\n" );
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document.write( "so, write your equation in vertex form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=%28-16t%5E2%2B38t%29%2B101 ALIGN=MIDDLE  ALT=\"H=%28-16t%5E2%2B38t%29%2B101\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   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=H=-16%28t%5E2-38t%2F16%29%2B101 ALIGN=MIDDLE  ALT=\"H=-16%28t%5E2-38t%2F16%29%2B101\"   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=H=-16%28t%5E2-19t%2F8%29%2B101 ALIGN=MIDDLE  ALT=\"H=-16%28t%5E2-19t%2F8%29%2B101\"   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=H=-16%28t%5E2-%2819%2F8%29%2Bb%5E2%29-%28-16%29b%5E2%2B101 ALIGN=MIDDLE  ALT=\"H=-16%28t%5E2-%2819%2F8%29%2Bb%5E2%29-%28-16%29b%5E2%2B101\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%2819%2F8%29%2F2=19%2F16 ALIGN=MIDDLE  ALT=\"b=%2819%2F8%29%2F2=19%2F16\"   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=H=-16%28t%5E2-19t%2F8%2B%2819%2F16%29%5E2%29%2B16%2819%2F16%29%5E2%2B101 ALIGN=MIDDLE  ALT=\"H=-16%28t%5E2-19t%2F8%2B%2819%2F16%29%5E2%29%2B16%2819%2F16%29%5E2%2B101\"   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=H=-16%28t-19%2F16%29%5E2%2B361%2F16%2B101 ALIGN=MIDDLE  ALT=\"H=-16%28t-19%2F16%29%5E2%2B361%2F16%2B101\"   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=H=-16%28t-19%2F16%29%5E2%2B1977%2F16 ALIGN=MIDDLE  ALT=\"H=-16%28t-19%2F16%29%5E2%2B1977%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> vertex is at(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19%2F16 ALIGN=MIDDLE  ALT=\"+19%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1977%2F16 ALIGN=MIDDLE  ALT=\"1977%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.19 ALIGN=MIDDLE  ALT=\"1.19\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=123.56 ALIGN=MIDDLE  ALT=\"123.56\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "so, the ball will reach max in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.19 ALIGN=MIDDLE  ALT=\"t=1.19\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds\r<BR>\n" );
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document.write( "2). <BR>\n" );
document.write( "the max height of the ball is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=123.56ft ALIGN=MIDDLE  ALT=\"123.56ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3.\r<BR>\n" );
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document.write( "the ball will return to the ground when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=0 ALIGN=MIDDLE  ALT=\"H=0\"   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=0=-16t%5E2%2B38t%2B101 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B38t%2B101\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > using quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"t=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16 ALIGN=MIDDLE  ALT=\"a=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=38 ALIGN=MIDDLE  ALT=\"+b=38\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=101 ALIGN=MIDDLE  ALT=\"c=101\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-38%2B-sqrt%2838%5E2-4%28-16%29%2A101%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t=%28-38%2B-sqrt%2838%5E2-4%28-16%29%2A101%29%29%2F%282%28-16%29%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=%28-38%2B-sqrt%281444%2B6464%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-38%2B-sqrt%281444%2B6464%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=%28-38%2B-sqrt%287908%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-38%2B-sqrt%287908%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=%28-38%2B-88.93%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-38%2B-88.93%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-38%2B88.93%29%2F%28-32%29=-1.59 ALIGN=MIDDLE  ALT=\"t=%28-38%2B88.93%29%2F%28-32%29=-1.59\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-38-88.93%29%2F%28-32%29=3.97 ALIGN=MIDDLE  ALT=\"t=%28-38-88.93%29%2F%28-32%29=3.97\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "disregard negative solution\r<BR>\n" );
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document.write( "so, the ball will return to the ground in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.97 ALIGN=MIDDLE  ALT=\"3.97\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );