document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=730246>Question 730246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown upward from the top of a building. The ball's height above the ground after t seconds is given by the function: h(t) = -16t^2 + 48t +32. \r<BR>\n" );
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document.write( "a. What is the initial height (i.e. the height of the building)?<BR>\n" );
document.write( "b. How high did the ball go?<BR>\n" );
document.write( "c. When does the ball hit the ground?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446587 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=446587\">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%28t%29+=+-16t%5E2+%2B+48t+%2B+32+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+%2B+48t+%2B+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "The instant the ball is thrown upward is<BR>\n" );
document.write( "called <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+0+ ALIGN=MIDDLE  ALT=\"+t+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug this value into the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+ ALIGN=MIDDLE  ALT=\"+h%280%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height of the building.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+-16%2A0+%2B+48%2A0+%2B+32+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+-16%2A0+%2B+48%2A0+%2B+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+32+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "The path of the ball is a parabola. The t-coordinate<BR>\n" );
document.write( "of the vertex is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+t%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the form<BR>\n" );
document.write( "is like the given equation<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-48%2F%28+2%2A%28-16%29%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-48%2F%28+2%2A%28-16%29%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%5Bv%5D+=+3%2F2+ ALIGN=MIDDLE  ALT=\"++t%5Bv%5D+=+3%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this back into equation to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5Bv%5D+ ALIGN=MIDDLE  ALT=\"+h%5Bv%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%5Bv%5D+=+-16%2A%283%2F2%29%5E2+%2B+48%2A%283%2F2%29+%2B+32+ ALIGN=MIDDLE  ALT=\"+h%5Bv%5D+=+-16%2A%283%2F2%29%5E2+%2B+48%2A%283%2F2%29+%2B+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5Bv%5D+=+-36+%2B+72+%2B+32+ ALIGN=MIDDLE  ALT=\"+h%5Bv%5D+=+-36+%2B+72+%2B+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5Bv%5D+=+68+ ALIGN=MIDDLE  ALT=\"+h%5Bv%5D+=+68+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The max height is 68 ft<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "The height is zero when it hits the ground, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-16t%5E2+%2B+48t+%2B+32+ ALIGN=MIDDLE  ALT=\"+0+=+-16t%5E2+%2B+48t+%2B+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%5E2+%2B+3t+%2B+2+=+0+ ALIGN=MIDDLE  ALT=\"+-t%5E2+%2B+3t+%2B+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-1+ ALIGN=MIDDLE  ALT=\"+a+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+3+ ALIGN=MIDDLE  ALT=\"+b+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+2+ ALIGN=MIDDLE  ALT=\"+c+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A%28-1%29%2A2+%29%29%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A%28-1%29%2A2+%29%29%2F%282%2A%28-1%29%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+=+%28-3+%2B-+sqrt%28+17+%29%29%2F%28-2%29%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-3+%2B-+sqrt%28+17+%29%29%2F%28-2%29%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+=+%28+3+%2B+sqrt%2817%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+3+%2B+sqrt%2817%29%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+3+%2B+4.123+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+3+%2B+4.123+%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+3.562+ ALIGN=MIDDLE  ALT=\"+t+=+3.562+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The ball hits the ground in 3.562 sec<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "Here's the plot of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-1%2C+5%2C+-5%2C+75%2C+-16x%5E2+%2B+48x+%2B+32%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-1%2C+5%2C+-5%2C+75%2C+-16x%5E2+%2B+48x+%2B+32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );