document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1080078>Question 1080078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find real numbers a,b and c so that the graph of the function <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;\" > contains the points (-1,5), (3,8) and (0,2)?\r<BR>\n" );
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document.write( "My process went as\r<BR>\n" );
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document.write( " (-1,5) is a point on the graph then values are, x=-1 and y=5 that must satisfy y=ax^2+bx+c<BR>\n" );
document.write( "Equation one being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%28-1%29%5E2%2Bb%28-1%29%2Bc=5+ ALIGN=MIDDLE  ALT=\"+a%28-1%29%5E2%2Bb%28-1%29%2Bc=5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " (3,8) is a point on the graph then values are, x=3 and y=8 that must satisfy y=ax^2+bx+c<BR>\n" );
document.write( "Equation two being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%283%29%5E2%2Bb%283%29%2Bc=8+ ALIGN=MIDDLE  ALT=\"+a%283%29%5E2%2Bb%283%29%2Bc=8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " (0,2) is a point on the graph then values are, x=0 and y=2 that must satisfy y=ax^2+bx+c<BR>\n" );
document.write( "Equation three being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%280%29%5E2%2Bb%280%29%2Bc=2+ ALIGN=MIDDLE  ALT=\"+a%280%29%5E2%2Bb%280%29%2Bc=2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that gives the system of 3 equation which are<BR>\n" );
document.write( "ONE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a-b%2Bc=5+ ALIGN=MIDDLE  ALT=\"+a-b%2Bc=5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "TWO <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9a%2B3b%2Bc=8 ALIGN=MIDDLE  ALT=\"+9a%2B3b%2Bc=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "THREE <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;\" >\r<BR>\n" );
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document.write( "then you start with ONE and THREE<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E2-b%2Bc=5+ ALIGN=MIDDLE  ALT=\"+a%5E2-b%2Bc=5+\"   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;\" > < multiply each side by -1<BR>\n" );
document.write( "and add to get a-b=3\r<BR>\n" );
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document.write( "Im not sure if thats the way to go where you then use equation 3 to eliminate c from equation 2 or if there's another process to get solutions of a, b and c? I'm thankful for any advice on 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 #694312 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=694312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First use the point of one of the given roots,  (0,2).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%2A0%5E2%2Bb%2A0%2Bc ALIGN=MIDDLE  ALT=\"y=a%2A0%5E2%2Bb%2A0%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=0%2B0%2Bc ALIGN=MIDDLE  ALT=\"2=0%2B0%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=2%29 ALIGN=MIDDLE  ALT=\"highlight%28c=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Make two equations with each of the other given points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx=y-c ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx=y-c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx=y-2 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx=y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A%28-1%29%5E2%2Bb%2A%28-1%29=5-2 ALIGN=MIDDLE  ALT=\"a%2A%28-1%29%5E2%2Bb%2A%28-1%29=5-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b=3 ALIGN=MIDDLE  ALT=\"a-b=3\"   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=a%2A3%5E2%2Bb%2A3=8-2 ALIGN=MIDDLE  ALT=\"a%2A3%5E2%2Bb%2A3=8-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%2B3b=6 ALIGN=MIDDLE  ALT=\"9a%2B3b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simplifiable,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2Bb=2 ALIGN=MIDDLE  ALT=\"3a%2Bb=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now solve this system:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a-b=3%2C2a%2Bb=2%29 ALIGN=MIDDLE  ALT=\"system%28a-b=3%2C2a%2Bb=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );