document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163445>Question 1163445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let x be the numbet of years since 1980 and y be the life expectancy for a person born between ( 1980 + x ) and ( 1980 + x + 5 ). Find the quadratic equation whose graph passess through the points  ( 0, 78,2) , ( 5, 79) and ( 10, 79.2 ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787539 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=787539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let x be the numbet of years since 1980 and y be the life expectancy for a person born between ( 1980 + x ) and ( 1980 + x + 5 ). Find the quadratic equation whose graph passess through the points  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%22%28+0%2C+78%2C2%29%22%29 ALIGN=MIDDLE  ALT=\"cross%28%22%28+0%2C+78%2C2%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (0,78.2), ( 5, 79) and ( 10, 79.2 )<br><BR>\n" );
document.write( "The general quadratic function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y+=+ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the three given data points in that equation to form three equations in the coefficients a, b, and c.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%280%5E2%29%2Bb%280%29%2Bc+=+78.2 ALIGN=MIDDLE  ALT=\"a%280%5E2%29%2Bb%280%29%2Bc+=+78.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+78.2 ALIGN=MIDDLE  ALT=\"c+=+78.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%285%5E2%29%2Bb%285%29%2Bc+=+79 ALIGN=MIDDLE  ALT=\"a%285%5E2%29%2Bb%285%29%2Bc+=+79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a%2B5b%2Bc+=+79 ALIGN=MIDDLE  ALT=\"25a%2B5b%2Bc+=+79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2810%5E2%29%2Bb%2810%29%2Bc+=+79.2 ALIGN=MIDDLE  ALT=\"a%2810%5E2%29%2Bb%2810%29%2Bc+=+79.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100a%2B10b%2Bc+=+79.2 ALIGN=MIDDLE  ALT=\"100a%2B10b%2Bc+=+79.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute (1) into (2) and (3) to get two equations in a and b.<br><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a%2B5b+=+0.8 ALIGN=MIDDLE  ALT=\"25a%2B5b+=+0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100a%2B10b+=+1 ALIGN=MIDDLE  ALT=\"100a%2B10b+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Subtract (4) from (5).<br><BR>\n" );
document.write( "{6) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75a%2B5b+=+0.2 ALIGN=MIDDLE  ALT=\"75a%2B5b+=+0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Subtract (4) from (6).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50a+=+-0.6 ALIGN=MIDDLE  ALT=\"50a+=+-0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(7) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-0.012+=+-3%2F250 ALIGN=MIDDLE  ALT=\"a+=+-0.012+=+-3%2F250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute in (4) to find b.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28-3%2F250%29%2B5b+=+0.8 ALIGN=MIDDLE  ALT=\"25%28-3%2F250%29%2B5b+=+0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F10+%2B+5b+=+8%2F10 ALIGN=MIDDLE  ALT=\"-3%2F10+%2B+5b+=+8%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5b+=+11%2F10 ALIGN=MIDDLE  ALT=\"5b+=+11%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+11%2F50 ALIGN=MIDDLE  ALT=\"b+=+11%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The quadratic equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-3%2F250%29x%5E2%2B%2811%2F50%29x%2B78.2 ALIGN=MIDDLE  ALT=\"y+=+%28-3%2F250%29x%5E2%2B%2811%2F50%29x%2B78.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );