document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=363181>Question 363181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you graph absolute value functions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258957 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=258957\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = 2|3x + 6| - 4\r<BR>\n" );
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document.write( "Finding the vertex:\r<BR>\n" );
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document.write( "1.  Set what's between the absolute value bars = 0\r<BR>\n" );
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document.write( "3x + 6 =  0<BR>\n" );
document.write( "    3x = -6<BR>\n" );
document.write( "     x = -2\r<BR>\n" );
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document.write( "That's the x-coordinate of the vertex.\r<BR>\n" );
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document.write( "2.  Substitute that in the equation to find the y-coordinate <BR>\n" );
document.write( "    of the vertex:\r<BR>\n" );
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document.write( "    y = 2|3(-2)+6| - 4<BR>\n" );
document.write( "    y = 2|-6+6| - 4<BR>\n" );
document.write( "    y = 2(0) - 4<BR>\n" );
document.write( "    y = -4\r<BR>\n" );
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document.write( "(Shortcut for this step: the y-coordinate of the vertex is<BR>\n" );
document.write( "just the number that's added to the absolute value term, in this<BR>\n" );
document.write( "case -4, because when you substitute the x-coordinate the <BR>\n" );
document.write( "absolute value term will always be 0)\r<BR>\n" );
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document.write( "3. The vertex is (-2,-4)\r<BR>\n" );
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document.write( "Plot that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28800%2F3%2C400%2C-5%2C5%2C-5%2C10%2C+graph%28800%2F3%2C400%2C-5%2C5%2C-5%2C10%29%2C%0D%0A+locate%28-2%2C-4%2C%22%28-2%2C-4%29%22%29%2C%0D%0A%0D%0Acircle%28-2%2C-4%2C.1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4. Find one other point, say the y-intercept, so let x=0,\r<BR>\n" );
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document.write( "y = 2|3(0) + 6| - 4<BR>\n" );
document.write( "y = 2|0 + 6| - 4<BR>\n" );
document.write( "y = 2|6| - 4<BR>\n" );
document.write( "y = 2(6) - 4<BR>\n" );
document.write( "y = 12 - 4<BR>\n" );
document.write( "y = 8<BR>\n" );
document.write( "    <BR>\n" );
document.write( "5. Plot the y-intercept (0,8)     \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28800%2F3%2C400%2C-5%2C5%2C-5%2C10%2C+graph%28800%2F3%2C400%2C-5%2C5%2C-5%2C10%29%2C%0D%0A+locate%28-2%2C-4%2C%22%28-2%2C-4%29%22%29%2C%0D%0A%0D%0Acircle%28-2%2C-4%2C.1%29%2Clocate%280%2C8%2C%22%280%2C8%29%22%29%2C%0D%0A%0D%0Acircle%280%2C8%2C.1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "6.  Draw a line through that point stopping at the vertex (-2,-4)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28800%2F3%2C400%2C-5%2C5%2C-5%2C10%2C+graph%28800%2F3%2C400%2C-5%2C5%2C-5%2C10%29%2C%0D%0A+locate%28-2%2C-4%2C%22%28-2%2C-4%29%22%29%2C%0D%0A%0D%0Acircle%28-2%2C-4%2C.1%29%2Clocate%280%2C8%2C%22%280%2C8%29%22%29%2C+green%28line%2810%2C68%2C-2%2C-4%29%29%2C%0D%0A%0D%0Acircle%280%2C8%2C.1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "7.  draw another line to make a symmetrical V-shaped graph, with vertex (-2,-4):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28800%2F3%2C400%2C-5%2C5%2C-5%2C10%2C+graph%28800%2F3%2C400%2C-5%2C5%2C-5%2C10%29%2C%0D%0A+locate%28-2%2C-4%2C%22%28-2%2C-4%29%22%29%2Cgreen%28line%2810%2C68%2C-2%2C-4%29%29%2C%0D%0A%0D%0A%0D%0Acircle%28-2%2C-4%2C.1%29%2Clocate%280%2C8%2C%22%280%2C8%29%22%29%2C+green%28line%28-8%2C32%2C-2%2C-4%29%29%2C%0D%0A%0D%0Acircle%280%2C8%2C.1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That's it!\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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