document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23655>Question 23655</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a quadratic function word problem. \r<BR>\n" );
document.write( "\n" );
document.write( "Solve for maximum height and graph.\r<BR>\n" );
document.write( "\n" );
document.write( "If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then its height is a function of time, given by s(t) = -16t^2 + 54t. Graph this function for 0 &#8804; t &#8804; 4. What is the maximum height reached by the ball?\r<BR>\n" );
document.write( "\n" );
document.write( "This problem is very confusing to me and any help will be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12442 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=12442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First: The general form of the equation for the height as a function of time of an object propelled upwards is given by: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+=+vot+%2B+ho ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+=+vot+%2B+ho\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: vo is the initial velocity at which the object is propelled and ho is the initial height from which the object is propelled.\r<BR>\n" );
document.write( "\n" );
document.write( "In your problem, since the ball (object) is propelled from the ground, the initial height (ho) is zero and the initial velocity of the ball is given as 64 feet/second so vo = 64. Your equation should read:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29+=+-16t%5E2+%2B+64t ALIGN=MIDDLE  ALT=\"s%28t%29+=+-16t%5E2+%2B+64t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The graph looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-10%2C75%2C-16x%5E2%2B64x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-10%2C75%2C-16x%5E2%2B64x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the curve is a parabola and it opens downward, the maximum height is to be found at the vertex of the parabola.<BR>\n" );
document.write( "The x-coordinate (this really corresponds to t in your equation) is given by: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-b%2F2a ALIGN=MIDDLE  ALT=\"t+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and in your equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29+=+-16t%5E2+%2B+64t ALIGN=MIDDLE  ALT=\"s%28t%29+=+-16t%5E2+%2B+64t\"   DISABLED_style= \"max-width:90%; height:auto;\" > a = -16 and b = 64. So the t-coordinate of the vertex is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-64%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+-64%2F2%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-64%2F-32 ALIGN=MIDDLE  ALT=\"t+=+-64%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2 ALIGN=MIDDLE  ALT=\"t+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > So the maximum height is attained at time t = 2 seconds.<BR>\n" );
document.write( "To find the value of the height  at this time, substitute t=2 into the original equation and solve for s.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29+=+-16%282%29%5E2+%2B+64%282%29 ALIGN=MIDDLE  ALT=\"s%282%29+=+-16%282%29%5E2+%2B+64%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29+=+-64+%2B+128 ALIGN=MIDDLE  ALT=\"s%282%29+=+-64+%2B+128\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29+=+64 ALIGN=MIDDLE  ALT=\"s%282%29+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. This is the maximum height.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );