document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174670>Question 174670</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618595554/algebrahomeworkh>Algebra 2, Texas Edition</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> During a halftime show, a baton twirler releases her baton from a point 4 feet above the ground with an initial vertical velocity of 25 feet per second. Use a vertical motion model to write a function for the height h (in feet) of the baton after t seconds then graph the function and label the vertex. <BR>\n" );
document.write( "Please show all work possible and any strategies used in depth. Thank You for your time and help! =) Hope to hear from you soon. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129692 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=129692\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can use the function for the height of an object propelled upwards with an initial velocity of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D ALIGN=MIDDLE  ALT=\"v%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > from an initial height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this problem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D+=+4 ALIGN=MIDDLE  ALT=\"h%5B0%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D+=+25 ALIGN=MIDDLE  ALT=\"v%5B0%5D+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so, making the substitutions, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2%2B25t%2B4 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2%2B25t%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can find the t-value of the vertex by:<BR>\n" );
document.write( "<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;\" > where: b = 25 and a = -16, so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-25%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-25%29%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+=+25%2F32 ALIGN=MIDDLE  ALT=\"t+=+25%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Let's look at the graph of this function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C15%2C-16x%5E2%2B25x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C15%2C-16x%5E2%2B25x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is the point at the top of the curve.<BR>\n" );
document.write( "Since we already have the t-value of the vertex, we can find the h-value by substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+25%2F32 ALIGN=MIDDLE  ALT=\"t+=+25%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the above equation and we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+881%2F64 ALIGN=MIDDLE  ALT=\"h+=+881%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the vertex is located at (0.78, 13.77) </SPAN>\n" );
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