document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939490>Question 939490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the parabola that passes through points (3.5,10), (11,60), and (15,90) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572480 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the parabola that passes through points (3.5,10), (11,60), and (15,90)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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;\" > ...we need to find coefficients <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;\" >; so, use given points and set the system of three quations \r<BR>\n" );
document.write( "\n" );
document.write( " for point (3.5,10) we have\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=a%283.5%29%5E2%2Bb%283.5%29%2Bc ALIGN=MIDDLE  ALT=\"10=a%283.5%29%5E2%2Bb%283.5%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=12.25a%2B%283.5%29b%2Bc ALIGN=MIDDLE  ALT=\"10=12.25a%2B%283.5%29b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " for point(11,60)  we have\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=a%2811%29%5E2%2Bb%2811%29%2Bc ALIGN=MIDDLE  ALT=\"60=a%2811%29%5E2%2Bb%2811%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=121a%2B11b%2Bc ALIGN=MIDDLE  ALT=\"60=121a%2B11b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for point (15,90) we have\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90=a%2815%29%5E2%2Bb%2815%29%2Bc ALIGN=MIDDLE  ALT=\"90=a%2815%29%5E2%2Bb%2815%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90=225a%2B15b%2Bc ALIGN=MIDDLE  ALT=\"90=225a%2B15b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve the system:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=12.25a%2B%283.5%29b%2Bc ALIGN=MIDDLE  ALT=\"10=12.25a%2B%283.5%29b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=121a%2B11b%2Bc ALIGN=MIDDLE  ALT=\"60=121a%2B11b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90=225a%2B15b%2Bc ALIGN=MIDDLE  ALT=\"90=225a%2B15b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.3<BR>\n" );
document.write( "------------------------------------------------------substitute eq.1 from eq.2\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60-10=121a%2B11b%2Bc-%2812.25a%2B%283.5%29b%2Bc%29 ALIGN=MIDDLE  ALT=\"60-10=121a%2B11b%2Bc-%2812.25a%2B%283.5%29b%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.2\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=121a%2B11b%2Bcross%28c%29-12.25a-%283.5%29b-cross%28c%29 ALIGN=MIDDLE  ALT=\"50=121a%2B11b%2Bcross%28c%29-12.25a-%283.5%29b-cross%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=108.75a%2B7.5b ALIGN=MIDDLE  ALT=\"50=108.75a%2B7.5b\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50-7.5b=108.75a ALIGN=MIDDLE  ALT=\"50-7.5b=108.75a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%2850-7.5b%29%2F108.75 ALIGN=MIDDLE  ALT=\"a=%2850-7.5b%29%2F108.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............1a\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute eq.2 from eq.3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90-60=225a%2B15b%2Bc-%28121a%2B11b%2Bc%29 ALIGN=MIDDLE  ALT=\"90-60=225a%2B15b%2Bc-%28121a%2B11b%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30=225a%2B15b%2Bc-121a-11b-c ALIGN=MIDDLE  ALT=\"30=225a%2B15b%2Bc-121a-11b-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30=104a%2B4b ALIGN=MIDDLE  ALT=\"30=104a%2B4b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%2830-4b%29%2F104 ALIGN=MIDDLE  ALT=\"a=%2830-4b%29%2F104\"   DISABLED_style= \"max-width:90%; height:auto;\" >............2a\r<BR>\n" );
document.write( "\n" );
document.write( "left sides in 1a and 2a are equal, so set  right sides   equal and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850-7.5b%29%2F108.75=%2830-4b%29%2F104 ALIGN=MIDDLE  ALT=\"%2850-7.5b%29%2F108.75=%2830-4b%29%2F104\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...cross multiply\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104%2850-7.5b%29=108.75%2830-4b%29 ALIGN=MIDDLE  ALT=\"104%2850-7.5b%29=108.75%2830-4b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5200-780b=3262.5-435b ALIGN=MIDDLE  ALT=\"5200-780b=3262.5-435b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5200-3262.5=780b+-435b ALIGN=MIDDLE  ALT=\"5200-3262.5=780b+-435b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1937.5=345b ALIGN=MIDDLE  ALT=\"1937.5=345b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1937.5%2F345 ALIGN=MIDDLE  ALT=\"b=1937.5%2F345\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5.615942028985507 ALIGN=MIDDLE  ALT=\"b=5.615942028985507\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5.6 ALIGN=MIDDLE  ALT=\"b=5.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "now 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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%2830-4b%29%2F104 ALIGN=MIDDLE  ALT=\"a=%2830-4b%29%2F104\"   DISABLED_style= \"max-width:90%; height:auto;\" >............2a\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%2830-4%2A5.6%29%2F104 ALIGN=MIDDLE  ALT=\"a=%2830-4%2A5.6%29%2F104\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%2830-22.4%29%2F104 ALIGN=MIDDLE  ALT=\"a=%2830-22.4%29%2F104\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=7.6%2F104 ALIGN=MIDDLE  ALT=\"a=7.6%2F104\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=76%2F1040 ALIGN=MIDDLE  ALT=\"a=76%2F1040\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0.0730769230769231 ALIGN=MIDDLE  ALT=\"a=0.0730769230769231\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0.07 ALIGN=MIDDLE  ALT=\"a=0.07\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now we can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=12.25a%2B%283.5%29b%2Bc ALIGN=MIDDLE  ALT=\"10=12.25a%2B%283.5%29b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.1\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=12.25%2A0.07%2B%283.5%295.6%2Bc ALIGN=MIDDLE  ALT=\"10=12.25%2A0.07%2B%283.5%295.6%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=0.8575%2B19.6%2Bc ALIGN=MIDDLE  ALT=\"10=0.8575%2B19.6%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=20.4575%2Bc ALIGN=MIDDLE  ALT=\"10=20.4575%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-20.4575=c ALIGN=MIDDLE  ALT=\"10-20.4575=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-10.4575 ALIGN=MIDDLE  ALT=\"c=-10.4575\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-10.5 ALIGN=MIDDLE  ALT=\"c=-10.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, your equation is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=0.07x%5E2%2B5.6x-10.5%29 ALIGN=MIDDLE  ALT=\"highlight%28y=0.07x%5E2%2B5.6x-10.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3.5,10), (11,60), and (15,90)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-15%2C+100%2C+-15%2C+100%2C%0D%0Acircle%283.5%2C10%2C.53%29%2Ccircle%2811%2C60%2C.53%29%2Ccircle%2815%2C90%2C.53%29%2C+%0D%0Alocate%283.5%2C10%2Cp%283.5%2C10%29%29%2Clocate%2811%2C60%2Cp%2811%2C60%29%29%2Clocate%2815%2C90%2Cp%2815%2C90%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-15%2C+100%2C+-15%2C+100%2C+0.07x%5E2%2B5.6x-10.5%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );