document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=101003>Question 101003</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395937787/algebrahomeworkh>algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> #18<BR>\n" );
document.write( "y=6 absolute value of x-7\r<BR>\n" );
document.write( "\n" );
document.write( "it says to gragh the function, identify the vertex,whether it opens up or down,and whether the graph is wider, narrower, or the same width as the graph of y= the absloute value of x<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73742 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=73742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The graphs that you are looking for are shown below. The red graph is the graph of y= 6|x-7| and<BR>\n" );
document.write( "the green graph is the graph of y = |x|.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that the red graph should be touching the x axis at the point x = 7. The graphing program<BR>\n" );
document.write( "apparently has a little difficulty in showing it as it should be. You can tell that y should<BR>\n" );
document.write( "be 0 when x is +7 by substituting +7 for x in the equation y = 6*|x-7|. When you substitute<BR>\n" );
document.write( "+7 for x the terms +7 and -7 inside the absolute value signs cancel to make the equation be<BR>\n" );
document.write( "y = 6*|0| and this reduces to y = 0.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C20%2C-5%2C+25%2C+6%2Aabs%28x-7%29%2C+abs%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C20%2C-5%2C+25%2C+6%2Aabs%28x-7%29%2C+abs%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the vertex is at (+7,0). As you can see, the graph opens up. And the graph of y = 6*|x-7| <BR>\n" );
document.write( "is narrower than the graph of y = |x|. This is because the absolute value quantity is<BR>\n" );
document.write( "multiplied by 6, so for a given value of x from the vertex, it rises 6 times faster. To<BR>\n" );
document.write( "demonstrate this we'll eliminate the multiplier of 6 and show the two graphs of y = |x-7| in<BR>\n" );
document.write( "red and y = |x| in green. Notice that without the multiplier of 6 the red graph is the same<BR>\n" );
document.write( "width as the green graph.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C20%2C-5%2C+25%2C+abs%28x-7%29%2C+abs%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C20%2C-5%2C+25%2C+abs%28x-7%29%2C+abs%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now that you have seen the graphs and have evaluated y when x equals +7 to find the vertex<BR>\n" );
document.write( "point of (7, 0), you can get other points on the graph by just assigning x some values in <BR>\n" );
document.write( "either direction from x = +7. For example, when x = 0, then y = 6*|0 - 7|, and the absolute<BR>\n" );
document.write( "value signs make this equation become y = 6*+7 = 42. Therefore you know that the point (0, 42)<BR>\n" );
document.write( "is on the graph.  And when x = +5 then y = 6*|5 - 7| = 6*|-2| = 6*2 = 12. So you know the point <BR>\n" );
document.write( "(5, 12) is on the graph. And when x = 8 then y = 6*|8 - 7| = 6*|-1| = 6*1 = 6. Therefore,<BR>\n" );
document.write( "the point (8, 6) is on the graph. You can continue this to get a sufficient number of<BR>\n" );
document.write( "points to allow you to draw the graph.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope the graphs help you to see what is going on in the problem.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );