document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486981>Question 486981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=x^2-2x-24\r<BR>\n" );
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document.write( "a - Determine the vertex?<BR>\n" );
document.write( "b - Does the graph open up or down?<BR>\n" );
document.write( "c - What is the equation of the axis of symmetry?<BR>\n" );
document.write( "d - Find any x-intercepts?<BR>\n" );
document.write( "e - Find the y-intercepts?<BR>\n" );
document.write( "f - Sketch the graph. <BR>\n" );
document.write( "g - State the domain and range in interval notation?\r<BR>\n" );
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document.write( "If you mess up one thing it makes you start over completely with a new problem, which what keeps happening to me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332895 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=332895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2-2x-24 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a - Determine the vertex?\r<BR>\n" );
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document.write( "Vertex Form of Equation  <BR>\n" );
document.write( "The vertex form of a parabola's equation is generally expressed as :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=+a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    (h,k) is the vertex\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2-2x-24 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-2x-24\"   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%5E2-2x%2B1+-25 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1+-25\"   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=%28x%5E2-2x%2B1%29+-25 ALIGN=MIDDLE  ALT=\"%28x%5E2-2x%2B1%29+-25\"   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=%28x-1%29%5E2-25 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,  (h,k) is  (1,-25) \r<BR>\n" );
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document.write( "b - Does the graph open up or down?\r<BR>\n" );
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document.write( "If a> 0, the parabola opens upwards<BR>\n" );
document.write( "        if a< 0, it opens downwards.\r<BR>\n" );
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document.write( "<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=a%3E+0 ALIGN=MIDDLE  ALT=\"a%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the parabola opens upwards\r<BR>\n" );
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document.write( "c - What is the equation of the axis of symmetry?\r<BR>\n" );
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document.write( " The axis of symmetry is the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   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+=+-%28-2%29%2F2%2A1 ALIGN=MIDDLE  ALT=\"x+=+-%28-2%29%2F2%2A1\"   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%2F2 ALIGN=MIDDLE  ALT=\"x+=+2%2F2\"   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+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d - Find any x-intercepts?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2-2x-24 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >....set <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-24=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x ALIGN=MIDDLE  ALT=\"-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-6x ALIGN=MIDDLE  ALT=\"4x-6x\"   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%5E2%2B4x-6x-24=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-6x-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%29-%286x%2B24%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%29-%286x%2B24%29=0\"   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%28x%2B4%29-6%28x%2B4%29=0 ALIGN=MIDDLE  ALT=\"x%28x%2B4%29-6%28x%2B4%29=0\"   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=%28x-6%29%28x%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6=0 ALIGN=MIDDLE  ALT=\"x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....->...<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;\" >.......one x-intercept is at (6,0)\r<BR>\n" );
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document.write( "if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4=0 ALIGN=MIDDLE  ALT=\"x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......other one x-intercept is at (-4,0)\r<BR>\n" );
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document.write( "e - Find the y-intercepts?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2-2x-24 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >....set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   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=f%28x%29=0%5E2-2%2A0-24 ALIGN=MIDDLE  ALT=\"f%28x%29=0%5E2-2%2A0-24\"   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=f%28x%29=-24 ALIGN=MIDDLE  ALT=\"f%28x%29=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >......<BR>\n" );
document.write( "so, y-intercept is at (0,-24)\r<BR>\n" );
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document.write( "f - Sketch the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-25%2C25%2C+-30%2C+20%2C+x%5E2-2x-24%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-25%2C25%2C+-30%2C+20%2C+x%5E2-2x-24%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "g - State the domain and range in interval notation? \r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=Plot_A_Graph_With_Domain.solver>Plot a graph of any function AND its DOMAIN</A></TD></TR>\n" );
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document.write( "  Here's a graph of function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-24 ALIGN=MIDDLE  ALT=\"x%5E2-2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > (x^2-2x-24). <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The domain is shown on the x axis by a <FONT COLOR=GREEN SIZE=+1>green horizontal line</FONT>.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-30%2C+30%2C+-30%2C+30%2C+x%5E2-2x-24%2C+domain%28+x%5E2-2x-24+%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " </SPAN>\n" );
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