document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23313>Question 23313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is my problem<BR>\n" );
document.write( "What is the \"Vertex\" & Sketch its graph\r<BR>\n" );
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document.write( "y = -3x^2 + 6x\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Paul </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12097 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12097\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are several ways to find the vertex of this.  I think the easiest way is to use a formula for the vertex that comes from the quadratic formula.  Remember that?   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Well, this formula is just the first part of this without the radical.  It turns out the vertex of a parabola <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;\" > (which opens up or down!) is always at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"x=-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In your case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3x%5E2+%2B+6x ALIGN=MIDDLE  ALT=\"y+=+-3x%5E2+%2B+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a=-3 and b=6, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-6%2F%282%28-3%29%29+=+1 ALIGN=MIDDLE  ALT=\"x=+-6%2F%282%28-3%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now, if x=1, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3x%5E2+%2B+6x ALIGN=MIDDLE  ALT=\"y+=+-3x%5E2+%2B+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3+%2B6=+3 ALIGN=MIDDLE  ALT=\"y=-3+%2B6=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Vertex is at (1,3).\r<BR>\n" );
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document.write( "Check it out with the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28500%2C500%2C+-10%2C10%2C-10%2C10%2C+-3x%5E2+%2B+6x%29+ ALIGN=MIDDLE  ALT=\"graph+%28500%2C500%2C+-10%2C10%2C-10%2C10%2C+-3x%5E2+%2B+6x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Does this graph look like the vertex is at (1,3), and does the graph open down?\r<BR>\n" );
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document.write( "R^2 at SCC. </SPAN>\n" );
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