document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109709>Question 1109709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Form quadratic functions given the following information:<BR>\n" );
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document.write( "f(3+ sqrt2 )=f(3&#8722;sqrt2 )=0; f(1)=&#8722;8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724797 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The roots are 3+sqrt(2) and 3-sqrt(2); that means the axis of symmetry is x=3; that means the vertex has x coordinate 3. Then the vertex form of the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-3%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-3%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then since y is 0 when x is 3+sqrt(2),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+a%28sqrt%282%29%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"0+=+a%28sqrt%282%29%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2a%2Bk ALIGN=MIDDLE  ALT=\"0+=+2a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (1)<br><BR>\n" );
document.write( "And since y is -8 when x is 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+=+a%28-2%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"-8+=+a%28-2%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+=+4a%2Bk ALIGN=MIDDLE  ALT=\"-8+=+4a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (2)<br><BR>\n" );
document.write( "Then from equations (1) and (2)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+=+2a ALIGN=MIDDLE  ALT=\"-8+=+2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-4 ALIGN=MIDDLE  ALT=\"a+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And then from either equation (1) or (2), k = 8.<br><BR>\n" );
document.write( "So the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-4%28x-3%29%5E2%2B8 ALIGN=MIDDLE  ALT=\"y+=+-4%28x-3%29%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-4%28x%5E2-6x%2B9%29%2B8 ALIGN=MIDDLE  ALT=\"y+=+-4%28x%5E2-6x%2B9%29%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-4x%5E2%2B24x-28 ALIGN=MIDDLE  ALT=\"y+=+-4x%5E2%2B24x-28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solving this equation using the quadratic formula verifies that the roots are 3 +/- sqrt(2); evaluating the expression for x=1 verifies that the y value is -8. </SPAN>\n" );
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