document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979388>Question 979388</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The quadratic function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > has the following characteristics: (i) passes through the point (2,4); (ii) has a maximum value of 6 when x=4; and (iii) has a zero of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2B2sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=4%2B2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Find the values of a,b, and c. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600652 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=600652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(4)=6\r<BR>\n" );
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document.write( "If there is a zero at 4+2 sqrt (3), there is a zero at 4 - 2 sqrt (3)<BR>\n" );
document.write( "a*4+b*2+c=4<BR>\n" );
document.write( "4a+2b+c=4\r<BR>\n" );
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document.write( "16a+4b+c=6<BR>\n" );
document.write( "Eliminate c<BR>\n" );
document.write( "4a+2b+c=4<BR>\n" );
document.write( "-16a-4b-c=-6<BR>\n" );
document.write( "-12a-2b=-2<BR>\n" );
document.write( "12a+2b=2<BR>\n" );
document.write( "6a+b=1<BR>\n" );
document.write( "But -b/2a=4, so -b=8a<BR>\n" );
document.write( "-2a=1<BR>\n" );
document.write( "a=(-1/2)<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "first equation -2+8+c=4; c=-2<BR>\n" );
document.write( "second equation -8+16+c=6; c=-2\r<BR>\n" );
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document.write( "(-1/2)x^2+4x-2=f(x)<BR>\n" );
document.write( "quadratic formula:<BR>\n" );
document.write( "{-4 +/- sqrt (16-4)}/-1<BR>\n" );
document.write( "roots are 4+/- sqrt (12); sqrt (12=2 sqrt (3))\r<BR>\n" );
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document.write( "a= -1/2<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "c= -2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%5E2%2B4x-2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%5E2%2B4x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );