document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=914436>Question 914436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given these two equations : f(x)=x^2-6x+9 and g(x)=-3x-5, change the slope of the line so that it will intersect the parabola in two locations.\r<BR>\n" );
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document.write( "What I have done so far:\r<BR>\n" );
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document.write( "Let f(x)=g(x)\r<BR>\n" );
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document.write( "x^2-6x+9=-3x-5<BR>\n" );
document.write( "x^2-3x+14=0\r<BR>\n" );
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document.write( "Then I calculated the discriminant to see how many solutions it would have.\r<BR>\n" );
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document.write( "D=b^2-4ac<BR>\n" );
document.write( "D=(-3)^2-4(1)(14)<BR>\n" );
document.write( "D=9-56<BR>\n" );
document.write( "D=-47\r<BR>\n" );
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document.write( "Since the discriminant is -47, therefore there are no real solutions to x^2-3x+14=0, which means that f(x) and g(x) never intersect.\r<BR>\n" );
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document.write( "What I did for the second part was represent the slope of the second equation with the variable \"m\".\r<BR>\n" );
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document.write( "f(x)=x^2-6x+9<BR>\n" );
document.write( "g(x)=mx-5\r<BR>\n" );
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document.write( "Let f(x)=g(x)\r<BR>\n" );
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document.write( "x^2-6x+9=mx-5<BR>\n" );
document.write( "x^2-6x-mx+9+5=0<BR>\n" );
document.write( "x^2-(6-m)x+14=0\r<BR>\n" );
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document.write( "a=1, b=-6-m, c=14\r<BR>\n" );
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document.write( "Sub a, b and c into discriminant equation\r<BR>\n" );
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document.write( "D=b^2-4ac<BR>\n" );
document.write( "D=(-6-m)(-6-m)-4(1)(14)<BR>\n" );
document.write( "D=36+6m+6m+m^2-56<BR>\n" );
document.write( "D=m^2+12m-20\r<BR>\n" );
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document.write( "This cannot be factored, so I don't know what to do next!\r<BR>\n" );
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document.write( "Thanks\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555105 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=555105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2-6x+9=mx-5  Good work<BR>\n" );
document.write( "x^2 - 6x - mx + 14 = 0<BR>\n" );
document.write( "x^2 -(6+m)x + 14 = <BR>\n" );
document.write( "Re: Discriminant<BR>\n" );
document.write( "(6+ m)^2 &#8805; 56<BR>\n" );
document.write( "m = 3, for ex: Line would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x-5 ALIGN=MIDDLE  ALT=\"y+=+3x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " (9)^2 &#8805; 56  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881-56%29+=+sqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2881-56%29+=+sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%289+%2B-+sqrt%28+25%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%289+%2B-+sqrt%28+25%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2,1) and (7,16 ) would be the solutions for this system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+++-10%2C10%2C-10%2C20%2C++%0D%0A+grid%281%29%2C%0D%0Acircle%282%2C+1%2C0.4%29%2C%0D%0Acircle%287%2C16%2C0.4%29%2C%0D%0Agraph%28+300%2C+300%2C+-10%2C10%2C-10%2C20%2C0%2C+x%5E2-6x%2B9%2C+0%2C3x+-+5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );