document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134725>Question 134725</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/061838670X/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am completely lost on how to do these. Any help would be great.<BR>\n" );
document.write( "It says:<BR>\n" );
document.write( "Sketch the graph of the following. Label vertex, x-and y-intercepts.<BR>\n" );
document.write( "f(x)=x^2-x-12\r<BR>\n" );
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document.write( "Vertex=( , )<BR>\n" );
document.write( "x-intercepts=( , );( , )<BR>\n" );
document.write( "y-intercept=( , ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98608 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=98608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your function is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1 ALIGN=MIDDLE  ALT=\"b=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-12 ALIGN=MIDDLE  ALT=\"c=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The vertex is located at the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28%28-b%29%2F2a%29 ALIGN=MIDDLE  ALT=\"f%28%28-b%29%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  So, calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5Bx%5D=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"v%5Bx%5D=%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the x-coordinate, then evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28v%5Bx%5D%29 ALIGN=MIDDLE  ALT=\"f%28v%5Bx%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the y-coordinate.  Plot this point on your graph.\r<BR>\n" );
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document.write( "The x-intercepts are at (p,0) and (q,0) where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=p ALIGN=MIDDLE  ALT=\"x=p\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=q ALIGN=MIDDLE  ALT=\"x=q\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the solutions to f(x)=0.  So solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+x+-+12+=+0 ALIGN=MIDDLE  ALT=\"+x%5E2+-+x+-+12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to determine p and q, then plot these two points.\r<BR>\n" );
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document.write( "The y-intercept is at (0,f(0)).  Evaluate f(0) by substituting 0 for x in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-12 ALIGN=MIDDLE  ALT=\"x%5E2-x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Plot this point.\r<BR>\n" );
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document.write( "Multiply the x-coordinate of the vertex by 2.  Symmetry of the curve about the vertical line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that there will be another point on the curve at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2Fa ALIGN=MIDDLE  ALT=\"%28-b%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29 ALIGN=MIDDLE  ALT=\"f%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >), i.e. 2 times the x-coordinate of the vertex and the y-coordinate of the y-intercept.  Plot this point.\r<BR>\n" );
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document.write( "Draw a smooth curve through the plotted points.  Done.\r<BR>\n" );
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document.write( "It should look something like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-14%2C14%2C-14%2C14%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28600%2C600%2C-14%2C14%2C-14%2C14%2Cx%5E2-x-12%29%2C%0D%0Acircle%284%2C0%2C.2%29%2C%0D%0Acircle%28-3%2C0%2C.2%29%2C%0D%0Acircle%281%2F2%2C-49%2F4%2C.2%29%2C%0D%0Acircle%280%2C-12%2C.2%29%2C%0D%0Acircle%281%2C-12%2C.2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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