document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10369>Question 10369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the height in feet for a ball thrown upward at 48 feet persecond is given by   s(t)=-16t2+48t, where t is the time in seconds after the ball is tossed. what is the maximum height that the ball will reach?\r<BR>\n" );
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document.write( "Please help me with this problem... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5548 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=5548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16t%5E2+%2B+46t ALIGN=MIDDLE  ALT=\"h+=+-16t%5E2+%2B+46t\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the equation for a parabola that opens downward. The quadratic equation is already in standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > where x = t, a = -16, b = 48, and c = 0.\r<BR>\n" );
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document.write( "The maximum height of the thrown object will be at the vertex (the maximumum value) (h, t) of the parabola.\r<BR>\n" );
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document.write( "The t-coordinate (equivalent to the x-coordnate) of the vertex (this is the time at which the object reaches its maximum height) is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%2F2a%29 ALIGN=MIDDLE  ALT=\"%28-b%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a = -16 and b = 48.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-48%29%2F2%28-16%29+=+3%2F2 ALIGN=MIDDLE  ALT=\"%28-48%29%2F2%28-16%29+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so, at t= 3/2 secs, the object is at its maximum height.<BR>\n" );
document.write( "To find the value of the maximum height at t = 3/2 secs, substitute t = 3/2 into the original quadratic equation and solve for h.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16%283%2F2%29%5E2+%2B+48%283%2F2%29 ALIGN=MIDDLE  ALT=\"h+=+-16%283%2F2%29%5E2+%2B+48%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16%289%2F4%29+%2B+48%283%2F2%29 ALIGN=MIDDLE  ALT=\"h+=+-16%289%2F4%29+%2B+48%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-36+%2B+72 ALIGN=MIDDLE  ALT=\"h+=+-36+%2B+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+36+ft ALIGN=MIDDLE  ALT=\"h+=+36+ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As a check, you could take the first derivative of the quadratic equation and set it to zero to find the value of t at the maximum height. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16t%5E2+%2B+48t ALIGN=MIDDLE  ALT=\"h+=+-16t%5E2+%2B+48t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dh%2Fdt+=+-32t+%2B+48 ALIGN=MIDDLE  ALT=\"dh%2Fdt+=+-32t+%2B+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32t+%2B+48+=+0 ALIGN=MIDDLE  ALT=\"-32t+%2B+48+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32t+=+-48 ALIGN=MIDDLE  ALT=\"-32t+=+-48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-48%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+-48%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >secs, same as previous answer for the time the object reaches maximum height.<BR>\n" );
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