document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978015>Question 978015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the cooordinates of the two points on the curve y=4-x^2 whose tangents pass through the point (-1,7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599520 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39627)</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=599520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The line  minus the parabola should have ONE solution.  Each of these lines must have slope  -2x, using derivative for the given parabola equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-7=%28-2x%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"y-7=%28-2x%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, equation for the tangent lines in point-slope form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%5E2-2x%2B7 ALIGN=MIDDLE  ALT=\"y=-2x%5E2-2x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----Again this is a TANGENT LINE, not a parabola.  We do not have yet any value for the slope.<BR>\n" );
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document.write( "This line must intersect the parabola in ONLY ONE POINT.  Their difference must be zero for only one value of x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2-2x%2B7-%284-x%5E2%29=0 ALIGN=MIDDLE  ALT=\"-2x%5E2-2x%2B7-%284-x%5E2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, difference between line and parabola.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2-2x%2B7-4%2Bx%5E2=0 ALIGN=MIDDLE  ALT=\"-2x%5E2-2x%2B7-4%2Bx%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2-2x%2B3=0 ALIGN=MIDDLE  ALT=\"-x%5E2-2x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-3=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x%2B3%29=0 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "One value where tangent on the parabola is x=1; and the other value where tangent on parabola is x=-3.\r<BR>\n" );
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document.write( "FIND CORRESPONDING y VALUES ON PARABOLA<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4-%281%29%5E2 ALIGN=MIDDLE  ALT=\"y=4-%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4-1 ALIGN=MIDDLE  ALT=\"y=4-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   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=y=4-%28-3%29%5E2 ALIGN=MIDDLE  ALT=\"y=4-%28-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4-9 ALIGN=MIDDLE  ALT=\"y=4-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The points where line is tangent to parabola and tangent includes  (-1,7)  are  (1,3)  and (-3,-5).\r<BR>\n" );
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document.write( "You can make a sketch, graph on your own to be more certain. </SPAN>\n" );
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