document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=694630>Question 694630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> rewrite function f(x)=-1/3x2-2x-9 in the form f(x)=a(x-h)2+k<BR>\n" );
document.write( "give x and y intercepts<BR>\n" );
document.write( "give domain and range </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #428100 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=428100\">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=-%281%2F3%29x%5E2-2x-9 ALIGN=MIDDLE  ALT=\"f%28x%29=-%281%2F3%29x%5E2-2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\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=completing_the_square.solver>Completing the Square to Get a Quadratic into Vertex Form</A></TD></TR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.333333333333333+x%5E2-2+x-9 ALIGN=MIDDLE  ALT=\"y=-0.333333333333333+x%5E2-2+x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x-intercept ALIGN=MIDDLE  ALT=\"+x-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%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=0=-%281%2F3%29x%5E2-2x-9 ALIGN=MIDDLE  ALT=\"0=-%281%2F3%29x%5E2-2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >...use quadratic formula to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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=x+=+%28-%28-2%29+%2B-+sqrt%28%28-2%29%5E2-4%2A%28-1%2F3%29%2A%28-9%29+%29%29%2F%282%2A%28-1%2F3%29%29+ ALIGN=MIDDLE   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+=+%282+%2B-+sqrt%284-12+%29%29%2F%28-2%2F3%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%284-12+%29%29%2F%28-2%2F3%29%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=x+=+%282+%2B-+sqrt%28-8+%29%29%2F%28-2%2F3%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28-8+%29%29%2F%28-2%2F3%29%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=x+=+%282+%2B-+2.83%2Ai%29%2F%28-2%2F3%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+2.83%2Ai%29%2F%28-2%2F3%29%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=x+=+3%282+%2B-+2.83%2Ai%29%2F-2+ ALIGN=MIDDLE  ALT=\"x+=+3%282+%2B-+2.83%2Ai%29%2F-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+=+%286+%2B-+8.49%2Ai%29%2F-2+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+8.49%2Ai%29%2F-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+=+%286%2F-2+%2B-+8.49%2Ai%2F-2%29+ ALIGN=MIDDLE  ALT=\"x+=+%286%2F-2+%2B-+8.49%2Ai%2F-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=x+=+-3+%2B-+4.245%2Ai+ ALIGN=MIDDLE  ALT=\"x+=+-3+%2B-+4.245%2Ai+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....so, we have two complex solutions, it means there is no real solutions and there is no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x-intercepts ALIGN=MIDDLE  ALT=\"+x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-intercept ALIGN=MIDDLE  ALT=\"y-intercept\"   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=-%281%2F3%290%5E2-2%2A0-9 ALIGN=MIDDLE  ALT=\"f%28x%29=-%281%2F3%290%5E2-2%2A0-9\"   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=0-0-9 ALIGN=MIDDLE  ALT=\"f%28x%29=0-0-9\"   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=-9 ALIGN=MIDDLE  ALT=\"f%28x%29=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-intercept ALIGN=MIDDLE  ALT=\"y-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "see it on a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C10%2C+-15%2C+10%2C+-%281%2F3%29x%5E2-2x-9%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C10%2C+-15%2C+10%2C+-%281%2F3%29x%5E2-2x-9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " domain:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \{\forall\,x\,|\,x\,\in\,\mathbb{R}\}\">\r<BR>\n" );
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document.write( " range:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{y\,|\,y\,\in\,\mathbb{R},\,y\ \leq\ -6\}\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );