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 #694322 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10555)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=694322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "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" );
document.write( "\n" );
document.write( "My process went as\r<BR>\n" );
document.write( "\n" );
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" );
document.write( "\n" );
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" );
document.write( "\n" );
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!<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">Great job in getting up to that point.<BR>\n" );
document.write( "a - b + c = 5 ----- eq (i)<BR>\n" );
document.write( "9a + 3b + c = 8 ----- eq (ii)<BR>\n" );
document.write( "c = 2 ------ eq (iii)<BR>\n" );
document.write( "Now, just substitute 2 for c in eq (i) to get: a – b = 3 ------- eq (iv)<BR>\n" );
document.write( "Then, substitute 2 for c in eq (ii) to get: 9a + 3b = 6, which reduces to 3a + b = 2 ------- eq (v)\r<BR>\n" );
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document.write( "Now, ADD eqs (v) & (iv) to ELIMINATE b<BR>\n" );
document.write( "From there, you should be able to find the values of a and b, you already have the value of c, so you have everything to form the equation. </SPAN>\n" );
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