document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=20867>Question 20867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the vertex and axis of symmetry in a quadratic equation?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10015 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE THE FOLLOWING 2 EXAMPLES TO KNOW THE METHOD\r<BR>\n" );
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document.write( "LET Y=X^2+4X+5..<BR>\n" );
document.write( "GRAPHICAL METHOD.....................<BR>\n" );
document.write( "GIVE DIFFERENT VALUES TO X AND FIND CORRESPONDING Y VALUE TABULATE..TAKE A SUITABLE SCALE AND PLOT FOR GRAPH<BR>\n" );
document.write( "X......0....1.......2....3....-1....-2....-3.....-4.......-5.........-6...........-7<BR>\n" );
document.write( "Y.....5....10.....17...26...2.....1.....2......5......10.........17..........26<BR>\n" );
document.write( "FROM TABLE/GRAPH YOU CAN SEE  THAT THE VERTEX IS AT X=-2 AND Y=1.....,AXIS OF SYMMETRY IS X=-2.......THERE IS A MINIMUM OF Y=1 AT THE VERTEX GIVEN ABOVE..........\r<BR>\n" );
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document.write( "ANALYTICALLY YOU CAN DO LIKE THIS<BR>\n" );
document.write( "Y=X^2+4X+4-4+5=(X+2)^2+1.....NOW (X+2)^2 BEING A SQUARE IS ALWAYS POSITIVE.SO ITS MINIMUM VALUE IS ZERO WHEN X=-2..AT THAT X=-2 ,MINIMUM VALUE OF Y OCCURS =0+1=1......NOW TAKING THIS AS VERTEX WE OBSERVE THAT ON EITHER SIDE OF X=-2,THAT IS SAY 5 UNITS ON EITHER SIDE OF X=-2...THAT IS X=-2+5=3 AND X=-2-5=-7......Y HAS SAME VALUE NAMELY (-7+2)^2+1=(-5)^2+1=26=(3+2)^2+1=5^2+1...SO X=-2 IS THE AXIS OF SYMMETRY....<BR>\n" );
document.write( "I HOPE YOU CAN DO THE SECOND PROBLEM BY YOUR SELF NOW WITH THESE EXAMPLES GIVEN TO YOU.<BR>\n" );
document.write( "VENUGOPAL<BR>\n" );
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document.write( "SEE RECENT ANSWERS GIVEN BY ME IN ALGEBRA.COM FOR THIS ...PROBLEM NO.20847,ANSWER NO.10010 DT 29TH.NOV.05....GIVEN BELOW\r<BR>\n" );
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document.write( "LET Y=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=+-x%5E2%2B4x-1+ ALIGN=MIDDLE  ALT=\"+f%28x%29=+-x%5E2%2B4x-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "GIVE DIFFERENT VALUES TO X IN THE ABOVE EQUATION AND FIND CORRESPONDING VALUES OF Y..TABULATE AS FOLLOWS,CHOOSE A SUITABLE SCALE AND PLOT THEM ON A GRAPH AS SHOWN BELOW<BR>\n" );
document.write( "X....0.....1......2.....3.......4......ETC..<BR>\n" );
document.write( "Y....-1....2......3.....2.......-1\r<BR>\n" );
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