document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114498>Question 1114498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value for c such that y = x + c is a tangent to the parabola <BR>\n" );
document.write( "y = x^2-x-12.\r<BR>\n" );
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document.write( "Can you please help me do questions like that? What is meant by 'tangent to the parabola'? \r<BR>\n" );
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document.write( "Thankyou </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729442 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=729442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---------------------------------------<BR>\n" );
document.write( "What is meant by 'tangent to the parabola'? <BR>\n" );
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document.write( "The line which touches but does not cross the parabola at the particular local point.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2-x-12 ALIGN=MIDDLE  ALT=\"y+=+x%5E2-x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dx%2Fdy=2x-1 ALIGN=MIDDLE  ALT=\"dx%2Fdy=2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Slope of a tangent line to the parabola is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1 ALIGN=MIDDLE  ALT=\"2x-1\"   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=mx%2Bc=%282x-1%29x%2Bc=1%2Ax%2Bc ALIGN=MIDDLE  ALT=\"y=mx%2Bc=%282x-1%29x%2Bc=1%2Ax%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "meaning, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1=1 ALIGN=MIDDLE  ALT=\"2x-1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=2 ALIGN=MIDDLE  ALT=\"2x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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( "The point on the parabola for x=1 is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-x-12 ALIGN=MIDDLE  ALT=\"y=x%5E2-x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1-1-12 ALIGN=MIDDLE  ALT=\"y=1-1-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-12 ALIGN=MIDDLE  ALT=\"y=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This point (1,-12) is both on the parabola and also on the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2Bc ALIGN=MIDDLE  ALT=\"y=x%2Bc\"   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=c=y-x ALIGN=MIDDLE  ALT=\"c=y-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-12-1 ALIGN=MIDDLE  ALT=\"c=-12-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=-13%29 ALIGN=MIDDLE  ALT=\"highlight%28c=-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The tangent line at that point:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=x-13%29 ALIGN=MIDDLE  ALT=\"highlight%28y=x-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-7%2C7%2C-13%2C1%2Cx%5E2-x-12%2Cx-13%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-7%2C7%2C-13%2C1%2Cx%5E2-x-12%2Cx-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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