document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173444>Question 173444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height in feet for a bal thrown upward at 48 feet per second is given by s(t)=-16t^2+48t, where t is the time in seconds after the ball is tossed what is the maximum height that the ball will reach? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128333 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128333\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29 ALIGN=MIDDLE  ALT=\"s%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get a parabola that is concave downward because the coefficient on the<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2 ALIGN=MIDDLE  ALT=\"t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is negative.  So, the maximum height will be reached at the time value coordinate of the vertex of the parabola and the maximum height will be the function value at the vertex.\r<BR>\n" );
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document.write( "The independent variable coordinate of the vertex of a parabola that is expressed in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Here, <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=48 ALIGN=MIDDLE  ALT=\"b=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the time value for the maximum height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-48%29%2F%28-32%29=3%2F2 ALIGN=MIDDLE  ALT=\"t=%28-48%29%2F%28-32%29=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find the actual maximum height, evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%283%2F2%29=-16%283%2F2%29%5E2%2B48%283%2F2%29=-16%289%2F4%29%2B48%283%2F2%29=-4%289%29%2B24%283%29=-36%2B72=36 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Answer: 36 feet.\r<BR>\n" );
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document.write( "The trouble with this problem is that you were given a function for the height of a thrown ball that only works in the very unlikely circumstance that the person throwing the ball is standing in a hole whose depth is exactly the height of his/her hand when he/she released the ball.  Under ordinary circumstances, a 6-foot tall person would release the ball somewhere in the neighborhood of 7 feet above the ground and therefore your function would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29=-16t%5E2%2B48t%2B7 ALIGN=MIDDLE  ALT=\"s%28t%29=-16t%5E2%2B48t%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Super-Double-Plus Extra Credit.\r<BR>\n" );
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document.write( "Assuming the same 7 feet above the ground release point, what would the s(t) function be if the ball were thrown upward at 64 feet per second initial velocity?\r<BR>\n" );
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document.write( "I just assumed that you needed the Algebra answer to this question.  If you need the Calculus method, write back. </SPAN>\n" );
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