document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139538>Question 1139538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the x intercepts and y intercepts of the absolute Value y=|x-2|-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760017 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=760017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "To find the y intercept, plug in x = 0 and simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+abs%28x-2%29+-+4 ALIGN=MIDDLE  ALT=\"y+=+abs%28x-2%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+abs%280-2%29+-+4 ALIGN=MIDDLE  ALT=\"y+=+abs%280-2%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every x with 0. From here we use the order of operations PEMDAS.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+abs%28-2%29+-+4 ALIGN=MIDDLE  ALT=\"y+=+abs%28-2%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2+-+4 ALIGN=MIDDLE  ALT=\"y+=+2+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2 ALIGN=MIDDLE  ALT=\"y+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y intercept is -2. This means the graph crosses the y axis at -2 on the vertical number line. This is the location (0,-2). See the graph below.\r<BR>\n" );
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document.write( "To find the x intercept(s), we replace y with 0 and solve for x. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+abs%28x-2%29+-+4 ALIGN=MIDDLE  ALT=\"y+=+abs%28x-2%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+abs%28x-2%29+-+4 ALIGN=MIDDLE  ALT=\"0+=+abs%28x-2%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B4+=+abs%28x-2%29+-+4%2B4 ALIGN=MIDDLE  ALT=\"0%2B4+=+abs%28x-2%29+-+4%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 4 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+abs%28x-2%29 ALIGN=MIDDLE  ALT=\"4+=+abs%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-2%29+=+4 ALIGN=MIDDLE  ALT=\"abs%28x-2%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2+=+4 ALIGN=MIDDLE  ALT=\"x-2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2+=+-4 ALIGN=MIDDLE  ALT=\"x-2+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > see note below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%2B2+=+4%2B2 ALIGN=MIDDLE  ALT=\"x-2%2B2+=+4%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%2B2+=+-4%2B2 ALIGN=MIDDLE  ALT=\"x-2%2B2+=+-4%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2 to both sides for each equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2 ALIGN=MIDDLE  ALT=\"x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The x intercepts are 6 and -2. In other words, the two x intercepts are at the locations (6,0) and (-2,0). These locations are where the graph crosses or touches the horizontal x axis. See the graph below.\r<BR>\n" );
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document.write( "note: I used the rule that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%29+=+k ALIGN=MIDDLE  ALT=\"abs%28x%29+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+k ALIGN=MIDDLE  ALT=\"x+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-k ALIGN=MIDDLE  ALT=\"x+=+-k\"   DISABLED_style= \"max-width:90%; height:auto;\" > where k is some positive number. For example, if k is replaced with 7 then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%29+=+7 ALIGN=MIDDLE  ALT=\"abs%28x%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > turns into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7 ALIGN=MIDDLE  ALT=\"x+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7 ALIGN=MIDDLE  ALT=\"x+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is because these two values (7 and -7) are both seven units away from the value 0 on the number line.\r<BR>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "<font color=red size=4>y intercept is -2</font><BR>\n" );
document.write( "<font color=red size=4>x intercepts are 6 and -2</font>\r<BR>\n" );
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document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/rugTLI8.png\"><BR>\n" );
document.write( "This V shaped graph is effectively two linear pieces \"glued\" together. The vertex is located at (2,-4). The graph was created with <a  rel=nofollow HREF= \"https://www.geogebra.org/\">GeoGebra</a> (free graphing software).<BR>\n" );
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