document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127715>Question 127715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I'm having trouble with this problem. Can you help me?\r<BR>\n" );
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document.write( "Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts. <BR>\n" );
document.write( "y = 2x^2 - 12x + 18<BR>\n" );
document.write( "( , ) (vertex)<BR>\n" );
document.write( "y = 	(y-intercept)<BR>\n" );
document.write( "x = 	(leftmost x-intercept)<BR>\n" );
document.write( "x = 	(rightmost x-intercept) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93569 by </B><A HREF=/tutors/aboutme.mpl?userid=HyperBrain><B>HyperBrain(694)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=HyperBrain><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=93569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Read first the lesson<BR>\n" );
document.write( "Shortcut in finding the vertex of any parabola\r<BR>\n" );
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document.write( "Ok, done?<BR>\n" );
document.write( "Let's start!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x%5E2+-+12x+%2B+18 ALIGN=MIDDLE  ALT=\"y+=+2x%5E2+-+12x+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Differentiating,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=4x-12 ALIGN=MIDDLE  ALT=\"dy%2Fdx=4x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equating to zero,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-12=0 ALIGN=MIDDLE  ALT=\"4x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=12 ALIGN=MIDDLE  ALT=\"4x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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( "Solving for y,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x%5E2+-+12x+%2B+18 ALIGN=MIDDLE  ALT=\"y+=+2x%5E2+-+12x+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%283%29%5E2-12%283%29%2B18 ALIGN=MIDDLE  ALT=\"y=2%283%29%5E2-12%283%29%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=18-36%2B18 ALIGN=MIDDLE  ALT=\"y=18-36%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y=0 and x=3 So,\r<BR>\n" );
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document.write( "The vertex is at (3,0)<BR>\n" );
document.write( "Let's check!<BR>\n" );
document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%281000%2C1000%2C-20%2C20%2C-20%2C20%2Cy+=+2x%5E2+-+12x+%2B+18%29 ALIGN=MIDDLE  ALT=\"graph%281000%2C1000%2C-20%2C20%2C-20%2C20%2Cy+=+2x%5E2+-+12x+%2B+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ok, we're correct!\r<BR>\n" );
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document.write( "Proceed,\r<BR>\n" );
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document.write( "to find the x-intercepts, let us equate y=0,\r<BR>\n" );
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document.write( "so,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E2+-+12x+%2B+18=0 ALIGN=MIDDLE  ALT=\"+2x%5E2+-+12x+%2B+18=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factoring,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > since this is a perfect square, there is only one x-intercept.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" >\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "the x-intercept is at (3,0).\r<BR>\n" );
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document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%281000%2C1000%2C-20%2C20%2C-20%2C20%2Cy+=+2x%5E2+-+12x+%2B+18%29 ALIGN=MIDDLE  ALT=\"graph%281000%2C1000%2C-20%2C20%2C-20%2C20%2Cy+=+2x%5E2+-+12x+%2B+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Done!<BR>\n" );
document.write( "Please watch our video http://www.metacafe.com/watch/1101445/science_avenue/\r<BR>\n" );
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document.write( "Power up,<BR>\n" );
document.write( "HyperBrain! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );