document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=535714>Question 535714</A>: <I><SPAN STYLE=\"word-break: break-all;\"> vertex form y=-x^2+6x+4 \r<BR>\n" );
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document.write( "i need in vertex form i cant find out how to do it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352103 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=352103\">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=-x%5E2%2B6x%2B4 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2B6x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Noticing that 6x is double the product of x and 3, I see the first two terms as part of a square. I add and subtract 9 (the square of 3), and group to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-x%5E2%2B6x-9%29%2B9%2B4 ALIGN=MIDDLE  ALT=\"y=%28-x%5E2%2B6x-9%29%2B9%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-3%29%5E2=-%28x%5E2-6x%2B9%29=-x%5E2%2B6x-9 ALIGN=MIDDLE  ALT=\"-%28x-3%29%5E2=-%28x%5E2-6x%2B9%29=-x%5E2%2B6x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and just \"completed the square.\"<BR>\n" );
document.write( "That gets me to the equation of the parabola in vertex form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28x-3%29%5E2%2B13 ALIGN=MIDDLE  ALT=\"y=-%28x-3%29%5E2%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That form of the equation equation tells you the axis of symmetry of the parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the vertex is at (3,13).<BR>\n" );
document.write( "To get the vertex form, you could \"complete the square\" as I did, or you could try to memorize an unwieldy formula handed down by someone who just did the same work with the generic parabola equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to come up with the formula for the vertex form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%2Bb%2F2a%29%5E2%2B%284ac-b%5E2%29%2F4a ALIGN=MIDDLE  ALT=\"y=a%28x%2Bb%2F2a%29%5E2%2B%284ac-b%5E2%29%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In your case, your a, b, and c values were:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <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" );
document.write( "If you substitute a, b and c in the monster formula you get your vertex form.<BR>\n" );
document.write( "Admittedly, there is an in-between way:<BR>\n" );
document.write( "You could just remember the formula for the axis: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "which gives you the x-coordinate for the vertex, calculate the value to know what to subtract from x in the vertex form, and then calculate the y-coordinate for the vertex, which is also the last term of the vertex form, by substituting the x-coordinate for the vertex in the equation for the parabola </SPAN>\n" );
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