document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005898>Question 1005898</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the quadratic function y&#65309;kx(x-2)+3. If its optimum value is 4, find the value of k. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622066 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=622066\">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=y=kx%5E2-2kx%2B3 ALIGN=MIDDLE  ALT=\"y=kx%5E2-2kx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C0 ALIGN=MIDDLE  ALT=\"k%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > where x is the middle value between the zeros.\r<BR>\n" );
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document.write( "Finding zeros using formula for general solution of quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282k%2B-+sqrt%284k%5E2-4k%2A3%29%29%2F%282k%29 ALIGN=MIDDLE  ALT=\"x=%282k%2B-+sqrt%284k%5E2-4k%2A3%29%29%2F%282k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "D for discriminant,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282k%2B-+sqrt%28D%29%29%2F%282k%29 ALIGN=MIDDLE  ALT=\"x=%282k%2B-+sqrt%28D%29%29%2F%282k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Middle x between the zeros is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k%2B2k%29%2F%282%2A2k%29 ALIGN=MIDDLE  ALT=\"%282k%2B2k%29%2F%282%2A2k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4k%2F4k ALIGN=MIDDLE  ALT=\"4k%2F4k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29 ALIGN=MIDDLE  ALT=\"highlight%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This means x=1 and y=4  is the maximum or \"optimum\" or VERTEX point for the function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=k%2A1%281-2%29%2B3 ALIGN=MIDDLE  ALT=\"4=k%2A1%281-2%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the given original equation or function<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=k%28-1%29%2B3 ALIGN=MIDDLE  ALT=\"4=k%28-1%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=-k%2B3 ALIGN=MIDDLE  ALT=\"4=-k%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=k-3 ALIGN=MIDDLE  ALT=\"-4=k-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-4%2B3 ALIGN=MIDDLE  ALT=\"k=-4%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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