document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172691>Question 172691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the given values to find an equation of the form f(x)= ax^2 + bx + c\r<BR>\n" );
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document.write( "1. f(0)= 5, f(1)=10, f(2)= 19 \r<BR>\n" );
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document.write( "Please explain step by step so I understand!\r<BR>\n" );
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document.write( "I would really appreciate any help!\r<BR>\n" );
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document.write( "Thank you very much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127548 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a function, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29 ALIGN=MIDDLE  ALT=\"f%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the value of the function evaluated at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You are given the values of the function evaluated at 0, 1, and 2.  So:\r<BR>\n" );
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document.write( "(1)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=5 ALIGN=MIDDLE  ALT=\"f%280%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%280%29%5E2%2Bb%280%29%2Bc=5 ALIGN=MIDDLE  ALT=\"a%280%29%5E2%2Bb%280%29%2Bc=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simplified <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5 ALIGN=MIDDLE  ALT=\"c=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(2)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=10 ALIGN=MIDDLE  ALT=\"f%281%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%29%5E2%2Bb%281%29%2Bc=10 ALIGN=MIDDLE  ALT=\"a%281%29%5E2%2Bb%281%29%2Bc=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simplified <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=10 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(3)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=19 ALIGN=MIDDLE  ALT=\"f%282%29=19\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%282%29%5E2%2Bb%282%29%2Bc=19 ALIGN=MIDDLE  ALT=\"a%282%29%5E2%2Bb%282%29%2Bc=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simplified <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b%2Bc=19 ALIGN=MIDDLE  ALT=\"4a%2B2b%2Bc=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since from (1) we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5 ALIGN=MIDDLE  ALT=\"c=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that can be substituted into (2) and (3), thus:\r<BR>\n" );
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document.write( "(4)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2B5=10 ALIGN=MIDDLE  ALT=\"a%2Bb%2B5=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > yielding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=5 ALIGN=MIDDLE  ALT=\"a%2Bb=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and,\r<BR>\n" );
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document.write( "(5)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b%2B5=19 ALIGN=MIDDLE  ALT=\"4a%2B2b%2B5=19\"   DISABLED_style= \"max-width:90%; height:auto;\" > yielding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b=14 ALIGN=MIDDLE  ALT=\"4a%2B2b=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > yielding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb=7 ALIGN=MIDDLE  ALT=\"2a%2Bb=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply (5) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "(6)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2a-b=-7 ALIGN=MIDDLE  ALT=\"-2a-b=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add (6) to (4) term-by-term:\r<BR>\n" );
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document.write( "(7)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2B0b=-2 ALIGN=MIDDLE  ALT=\"-a%2B0b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into (4):\r<BR>\n" );
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document.write( "(8)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Bb=5 ALIGN=MIDDLE  ALT=\"2%2Bb=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you can say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E2%2B3x%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E2%2B3x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > by substituting the values determined 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;\" >, <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;\" > when the system of linear equations was solved.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=2%280%29%5E2%2B3%280%29%2B5=0%2B0%2B5=5 ALIGN=MIDDLE  ALT=\"f%280%29=2%280%29%5E2%2B3%280%29%2B5=0%2B0%2B5=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Check\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2%281%29%5E2%2B3%281%29%2B5=2%2B3%2B5=10 ALIGN=MIDDLE  ALT=\"f%281%29=2%281%29%5E2%2B3%281%29%2B5=2%2B3%2B5=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Check\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=2%282%29%5E2%2B3%282%29%2B5=8%2B6%2B5=19 ALIGN=MIDDLE  ALT=\"f%282%29=2%282%29%5E2%2B3%282%29%2B5=8%2B6%2B5=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Check </SPAN>\n" );
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