document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=759456>Question 759456</A>: <I><SPAN STYLE=\"word-break: break-all;\">   The graph of a quadratic function passes through B(4,6), and the zeros of the function are 5 and 6.  Write an equation of the graph in general form.\r<BR>\n" );
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document.write( "This question makes no sense.  If the x-intercepts are 5 and 6 how can there be a point (4,6) and still be a quadratic function.  HELP please. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #462040 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=462040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Generally you would have y=ax^2+bx+c, and you are given the two zeros of the parabola.  Try to narrow some of the equation using them.\r<BR>\n" );
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document.write( "Point (5,0):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%2A5%2A5%2Bb%2A5%2Bc ALIGN=MIDDLE  ALT=\"0=a%2A5%2A5%2Bb%2A5%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a%2B5b%2Bc=0 ALIGN=MIDDLE  ALT=\"25a%2B5b%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Point (6,0):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A6%2A6%2Bb%2A6%2Bc=0 ALIGN=MIDDLE  ALT=\"a%2A6%2A6%2Bb%2A6%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36a%2B6b%2Bc=0 ALIGN=MIDDLE  ALT=\"36a%2B6b%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also you were given point B(4,6):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A4%2A4%2Bb%2A4%2Bc=6 ALIGN=MIDDLE  ALT=\"a%2A4%2A4%2Bb%2A4%2Bc=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16a%2B4b%2Bc=6 ALIGN=MIDDLE  ALT=\"16a%2B4b%2Bc=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOW you have a system of three equations in three unknowns (yes, they should be constants but currently you do not know their values) of a, b, and c.<BR>\n" );
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document.write( "SYSTEM:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16a%2B4b%2Bc=6 ALIGN=MIDDLE  ALT=\"16a%2B4b%2Bc=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36a%2B6b%2Bc=0 ALIGN=MIDDLE  ALT=\"36a%2B6b%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a%2B5b%2Bc=0 ALIGN=MIDDLE  ALT=\"25a%2B5b%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------\r<BR>\n" );
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document.write( "Can you take the rest of the solution process from there?\r<BR>\n" );
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document.write( "Omitting the steps in solving that system, I found:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-33 ALIGN=MIDDLE  ALT=\"b=-33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=90 ALIGN=MIDDLE  ALT=\"c=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "EQUATION: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=3x%5E2-33x%2B90%29 ALIGN=MIDDLE  ALT=\"highlight%28y=3x%5E2-33x%2B90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "{solution checks as correct}. </SPAN>\n" );
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