document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170723>Question 1170723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is hit into the air from a height of 4 feet.  The function g(t)=-16t^2+120t+4 can be used to model the height of the ball where t is the time in seconds after the ball is hit.  <BR>\n" );
document.write( "a.About how long is the ball in the air?<BR>\n" );
document.write( "b.When is the ball back to 4 feet off the ground?<BR>\n" );
document.write( "c.How high is the ball after 4 seconds?<BR>\n" );
document.write( "d.When is the ball 150 feet in the air?<BR>\n" );
document.write( "e.What is the maximum height the ball reaches?  How many seconds does it take for this max to occur? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795604 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=795604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. About how long is the ball in the air?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28t%29=0 ALIGN=MIDDLE  ALT=\"g%28t%29=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%2B120t%2B4 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B120t%2B4\"   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-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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-120%2B-sqrt%28120%5E2-4%28-16%294%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t=%28-120%2B-sqrt%28120%5E2-4%28-16%294%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=%28-120%2B-sqrt%2814656%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-120%2B-sqrt%2814656%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=%28-120%2B-121.06%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-120%2B-121.06%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "need only positive solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-120-121.06%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-120-121.06%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 ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8773; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.53 ALIGN=MIDDLE  ALT=\"7.53\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds\r<BR>\n" );
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document.write( "b. When is the ball back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet off the ground?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28t%29=4 ALIGN=MIDDLE  ALT=\"g%28t%29=4\"   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=4=-16t%5E2%2B120t%2B4 ALIGN=MIDDLE  ALT=\"4=-16t%5E2%2B120t%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=-4t%5E2%2B30t%2B1 ALIGN=MIDDLE  ALT=\"1=-4t%5E2%2B30t%2B1\"   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=-4t%5E2%2B30t%2B1-1 ALIGN=MIDDLE  ALT=\"0=-4t%5E2%2B30t%2B1-1\"   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=-4t%5E2%2B30t ALIGN=MIDDLE  ALT=\"0=-4t%5E2%2B30t\"   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=-4t%28t-30%2F4%29 ALIGN=MIDDLE  ALT=\"0=-4t%28t-30%2F4%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=0=-4t%28t-15%2F2%29 ALIGN=MIDDLE  ALT=\"0=-4t%28t-15%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "need only positive solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28t-15%2F2%29 ALIGN=MIDDLE  ALT=\"0=%28t-15%2F2%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=15%2F2 ALIGN=MIDDLE  ALT=\"t=15%2F2\"   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=7.5 ALIGN=MIDDLE  ALT=\"t=7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds\r<BR>\n" );
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document.write( "c. How high is the ball after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4 ALIGN=MIDDLE  ALT=\"t=4\"   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=g%284%29=-16%2A4%5E2%2B120%2A4%2B4 ALIGN=MIDDLE  ALT=\"g%284%29=-16%2A4%5E2%2B120%2A4%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%284%29=228 ALIGN=MIDDLE  ALT=\"g%284%29=228\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet\r<BR>\n" );
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document.write( "d. When is the ball <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150 ALIGN=MIDDLE  ALT=\"150\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet in the air?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28t%29=150 ALIGN=MIDDLE  ALT=\"g%28t%29=150\"   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=150=-16t%5E2%2B120t%2B4 ALIGN=MIDDLE  ALT=\"150=-16t%5E2%2B120t%2B4\"   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%2B120t%2B4-150 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B120t%2B4-150\"   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%2B120t-146 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B120t-146\"   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=%28-120%2B-sqrt%28120%5E2-4%28-16%29%28-146%29%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t=%28-120%2B-sqrt%28120%5E2-4%28-16%29%28-146%29%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=%28-120%2B-sqrt%285056%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-120%2B-sqrt%285056%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "need only positive solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-120%2B-71.1%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-120%2B-71.1%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=%28-120-71.1%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-120-71.1%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=5.971875 ALIGN=MIDDLE  ALT=\"t=5.971875\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8773; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.97 ALIGN=MIDDLE  ALT=\"5.97\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds\r<BR>\n" );
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document.write( "e. What is the maximum height the ball reaches? How many seconds does it take for this max to occur?\r<BR>\n" );
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document.write( "max is at vertex, write 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=g%28x%29=-16t%5E2%2B120t%2B4 ALIGN=MIDDLE  ALT=\"g%28x%29=-16t%5E2%2B120t%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28-16t%5E2%2B120t%29%2B4 ALIGN=MIDDLE  ALT=\"g%28x%29=%28-16t%5E2%2B120t%29%2B4\"   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=g%28x%29=-16%28t%5E2-%2815%2F2%29t%29%2B4 ALIGN=MIDDLE  ALT=\"g%28x%29=-16%28t%5E2-%2815%2F2%29t%29%2B4\"   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=g%28x%29=-16%28t%5E2-%2815%2F2%29t%2Bb%5E2%29-%28-16b%5E2%29%2B4 ALIGN=MIDDLE  ALT=\"g%28x%29=-16%28t%5E2-%2815%2F2%29t%2Bb%5E2%29-%28-16b%5E2%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%2815%2F2%29%2F2=15%2F4 ALIGN=MIDDLE  ALT=\"b=%2815%2F2%29%2F2=15%2F4\"   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=g%28x%29=-16%28t%5E2-%2815%2F2%29t%2B%2815%2F4%29%5E2%29-%28-16%2815%2F4%29%5E2%29%2B4 ALIGN=MIDDLE  ALT=\"g%28x%29=-16%28t%5E2-%2815%2F2%29t%2B%2815%2F4%29%5E2%29-%28-16%2815%2F4%29%5E2%29%2B4\"   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=g%28x%29=-16%28t-15%2F4%29%5E2%2B16%28225%2F16%29%2B4 ALIGN=MIDDLE  ALT=\"g%28x%29=-16%28t-15%2F4%29%5E2%2B16%28225%2F16%29%2B4\"   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=g%28x%29=-16%28t-15%2F4%29%5E2%2B225%2B4 ALIGN=MIDDLE  ALT=\"g%28x%29=-16%28t-15%2F4%29%5E2%2B225%2B4\"   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=g%28x%29=-16%28t-15%2F4%29%5E2%2B229 ALIGN=MIDDLE  ALT=\"g%28x%29=-16%28t-15%2F4%29%5E2%2B229\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=15%2F4 ALIGN=MIDDLE  ALT=\"h=15%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=229 ALIGN=MIDDLE  ALT=\"k=229\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "vetex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F4 ALIGN=MIDDLE  ALT=\"15%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=229 ALIGN=MIDDLE  ALT=\"229\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "max is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=229 ALIGN=MIDDLE  ALT=\"229\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and it will take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F4 ALIGN=MIDDLE  ALT=\"15%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds for this max to occur\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );