document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147844>Question 147844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jake Johnson dives off the high dive at a pool. His distance from the surface of the water varies quadratically with the number of seconds that have passed since he left the board. His distances at times of 1, 2, and 3 seconds since he left the board are 24, 18, and 2 meters above the water, respectively.<BR>\n" );
document.write( "How do you write the particular equation expressing distance in terms of time? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108250 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=108250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is distance, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a funtion of time<BR>\n" );
document.write( "Here is the most general way to express it as a quadratic:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28t%29++=+a%2At%5E2+%2B+b%2At+%2B+c ALIGN=MIDDLE  ALT=\"d%28t%29++=+a%2At%5E2+%2B+b%2At+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > different snapshots of the dive, so that<BR>\n" );
document.write( "should give me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > equations, and I should be able to<BR>\n" );
document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+a%2A%281%29%5E2+%2B+b%2A%281%29+%2B+c ALIGN=MIDDLE  ALT=\"24+=+a%2A%281%29%5E2+%2B+b%2A%281%29+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+=+a%2A%282%29%5E2+%2B+b%2A%282%29+%2B+c ALIGN=MIDDLE  ALT=\"18+=+a%2A%282%29%5E2+%2B+b%2A%282%29+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+a%2A%283%29%5E2+%2B+b%2A%283%29+%2B+c ALIGN=MIDDLE  ALT=\"2+=+a%2A%283%29%5E2+%2B+b%2A%283%29+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now figure out the square terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+a+%2B+b+%2B+c ALIGN=MIDDLE  ALT=\"24+=+a+%2B+b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+=+4a+%2B+2b+%2B+c ALIGN=MIDDLE  ALT=\"18+=+4a+%2B+2b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+9a+%2B+3b+%2B+c ALIGN=MIDDLE  ALT=\"2+=+9a+%2B+3b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll multiply the 2nd equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the 3rd one by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54+=+12a+%2B+6b%2B+3c ALIGN=MIDDLE  ALT=\"54+=+12a+%2B+6b%2B+3c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+18a+%2B+6b+%2B+2c ALIGN=MIDDLE  ALT=\"4+=+18a+%2B+6b+%2B+2c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now subtract<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50+=+-6a+%2B+c ALIGN=MIDDLE  ALT=\"50+=+-6a+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now subtract the 1st from the 2nd<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+3a+%2B+b+ ALIGN=MIDDLE  ALT=\"-6+=+3a+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12+=+6a+%2B+2b ALIGN=MIDDLE  ALT=\"-12+=+6a+%2B+2b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38+=+2b+%2B+c ALIGN=MIDDLE  ALT=\"38+=+2b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract thre 3rd one from this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+-9a+-+b ALIGN=MIDDLE  ALT=\"36+=+-9a+-+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-9a+-+36 ALIGN=MIDDLE  ALT=\"b+=+-9a+-+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+3a+%2B+%28-9a+-+36%29 ALIGN=MIDDLE  ALT=\"-6+=+3a+%2B+%28-9a+-+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+3a+-+9a+-+36 ALIGN=MIDDLE  ALT=\"-6+=+3a+-+9a+-+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6a+=+-30 ALIGN=MIDDLE  ALT=\"6a+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-5 ALIGN=MIDDLE  ALT=\"a+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50+=+-6%2A%28-5%29+%2B+c ALIGN=MIDDLE  ALT=\"50+=+-6%2A%28-5%29+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50+=+30+%2B+c ALIGN=MIDDLE  ALT=\"50+=+30+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+20 ALIGN=MIDDLE  ALT=\"c+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38+=+2b+%2B+20 ALIGN=MIDDLE  ALT=\"38+=+2b+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b+=+18 ALIGN=MIDDLE  ALT=\"2b+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+9 ALIGN=MIDDLE  ALT=\"b+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the equation I come up with is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28t%29++=+a%2At%5E2+%2B+b%2At+%2B+c ALIGN=MIDDLE  ALT=\"d%28t%29++=+a%2At%5E2+%2B+b%2At+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28t%29+=+-5t%5E2+%2B+9t+%2B+20 ALIGN=MIDDLE  ALT=\"d%28t%29+=+-5t%5E2+%2B+9t+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "Let's see if it satisfies the data given<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%281%29+=+-5%2A1%5E2+%2B+9%2A1+%2B+20 ALIGN=MIDDLE  ALT=\"d%281%29+=+-5%2A1%5E2+%2B+9%2A1+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+-5+%2B+9+%2B+20 ALIGN=MIDDLE  ALT=\"24+=+-5+%2B+9+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+24 ALIGN=MIDDLE  ALT=\"24+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%282%29+=+-5%2A2%5E2+%2B+9%2A2+%2B+20 ALIGN=MIDDLE  ALT=\"d%282%29+=+-5%2A2%5E2+%2B+9%2A2+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+=+-20+%2B+18+%2B+20 ALIGN=MIDDLE  ALT=\"18+=+-20+%2B+18+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+=+18 ALIGN=MIDDLE  ALT=\"18+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%283%29+=+-5%2A3%5E2+%2B+9%2A3+%2B+20 ALIGN=MIDDLE  ALT=\"d%283%29+=+-5%2A3%5E2+%2B+9%2A3+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+-45+%2B+27+%2B+20 ALIGN=MIDDLE  ALT=\"2+=+-45+%2B+27+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+2 ALIGN=MIDDLE  ALT=\"2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );