document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=327596>Question 327596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a quadratic equation f(x) = ax^2+bx+c whose graph has a maximum value at 25 and x-intercepts -3 and 2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #234641 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=234641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=C%28x%2B3%29%28x-2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x%2B3%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where C is a constant to be determined using the maximum value of 25.<BR>\n" );
document.write( "Move from this general form to the vertex form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2FC=x%5E2-2x%2B3x-6 ALIGN=MIDDLE  ALT=\"f%28x%29%2FC=x%5E2-2x%2B3x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2FC=x%5E2%2Bx-6 ALIGN=MIDDLE  ALT=\"f%28x%29%2FC=x%5E2%2Bx-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2FC=%28x%5E2%2Bx%2B1%2F4%29-6-1%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29%2FC=%28x%5E2%2Bx%2B1%2F4%29-6-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2FC=%28x%2B1%2F2%29%5E2-25%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29%2FC=%28x%2B1%2F2%29%5E2-25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=C%28x%2B1%2F2%29%5E2-%2825C%29%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x%2B1%2F2%29%5E2-%2825C%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex of the equation is (-1/2,-25C/4) and the maximum occurs at the vertex.<BR>\n" );
document.write( "For the maximum value equal to 25,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2825C%29%2F4=25 ALIGN=MIDDLE  ALT=\"-%2825C%29%2F4=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-4 ALIGN=MIDDLE  ALT=\"C=-4\"   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=f%28x%29=-4x%5E2-4x%2B24 ALIGN=MIDDLE  ALT=\"f%28x%29=-4x%5E2-4x%2B24\"   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=drawing%28300%2C300%2C-5%2C5%2C-5%2C30%2Cgrid%281%29%2Ccircle%28-3%2C0%2C.2%29%2Ccircle%282%2C0%2C.2%29%2Ccircle%28-1%2F2%2C25%2C0.2%29%2Cgraph%28300%2C300%2C-5%2C5%2C-5%2C30%2C-4x%5E2-4x%2B24%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );