document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=907730>Question 907730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An object projected from height of 48 ft. with an initial velocity of 32 ft./sec after t seconds has a height = -16t^2 + 32t +48.<BR>\n" );
document.write( "A) After how many seconds is the height 64 ft?<BR>\n" );
document.write( "B) After how many seconds does the object hit the ground?<BR>\n" );
document.write( "C) How high is the object after 1/2 second?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'm not entirely confident with my answers but here is what I got:<BR>\n" );
document.write( "A) 1 second<BR>\n" );
document.write( "B) 3 seconds<BR>\n" );
document.write( "C) 60 feet<BR>\n" );
document.write( "I just need help to see if I understood this correctly. I was having a very difficult time 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 #550531 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE REASONING:<BR>\n" );
document.write( "A) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28height+=+-16t%5E2+%2B+32t+%2B48%2C+height=64%29 ALIGN=MIDDLE  ALT=\"system%28height+=+-16t%5E2+%2B+32t+%2B48%2C+height=64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64=+-16t%5E2+%2B+32t+%2B48 ALIGN=MIDDLE  ALT=\"64=+-16t%5E2+%2B+32t+%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You solved that equation correctly and found <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "B) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28height+=+-16t%5E2+%2B+32t+%2B48%2C+height=0%29 ALIGN=MIDDLE  ALT=\"system%28height+=+-16t%5E2+%2B+32t+%2B48%2C+height=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-16t%5E2+%2B+32t+%2B48 ALIGN=MIDDLE  ALT=\"0=+-16t%5E2+%2B+32t+%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You solved that equation correctly and found <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "C) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28height+=+-16t%5E2+%2B+32t+%2B48%2C+t=1%2F2%29 ALIGN=MIDDLE  ALT=\"system%28height+=+-16t%5E2+%2B+32t+%2B48%2C+t=1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=height+=+-16%281%2F2%29%5E2+%2B+32%281%2F2%29+%2B48=-16%281%2F4%29%2B16%2B48=-4%2B16-48=60 ALIGN=MIDDLE  ALT=\"height+=+-16%281%2F2%29%5E2+%2B+32%281%2F2%29+%2B48=-16%281%2F4%29%2B16%2B48=-4%2B16-48=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and you did the calculation correctly.<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE QUADRATIC EQUATIONS:<BR>\n" );
document.write( "There are many ways to solve. This is my way.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64=+-16t%5E2+%2B+32t+%2B48 ALIGN=MIDDLE  ALT=\"64=+-16t%5E2+%2B+32t+%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64-48=+-16t%5E2+%2B+32t ALIGN=MIDDLE  ALT=\"64-48=+-16t%5E2+%2B+32t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=+-16t%5E2+%2B+32t ALIGN=MIDDLE  ALT=\"16=+-16t%5E2+%2B+32t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Here I would say that I am dividing both sides of the equal sign by -16, <BR>\n" );
document.write( "but I think of it as two steps)<BR>\n" );
document.write( "Dividing both sides of the equation by 16, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=-t%5E2%2B2 ALIGN=MIDDLE  ALT=\"1=-t%5E2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and changing the signs (multiplying both sides times -1), we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-2t=-1 ALIGN=MIDDLE  ALT=\"t%5E2-2t=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding 1 to both sides, I complete the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-2t%2B1=-1%2B1 ALIGN=MIDDLE  ALT=\"t%5E2-2t%2B1=-1%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t-1%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28t-1%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-1=0 ALIGN=MIDDLE  ALT=\"t-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-16t%5E2+%2B+32t+%2B48 ALIGN=MIDDLE  ALT=\"0=+-16t%5E2+%2B+32t+%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides by -16, I would get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-2t-3=0 ALIGN=MIDDLE  ALT=\"t%5E2-2t-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-2t=3 ALIGN=MIDDLE  ALT=\"t%5E2-2t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-2t%2B1=3%2B1 ALIGN=MIDDLE  ALT=\"t%5E2-2t%2B1=3%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t-1%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28t-1%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-1=2 ALIGN=MIDDLE  ALT=\"t-1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );