document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315287>Question 315287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what value of b will the line y=-2x+b be tangent to the parabola y=3x^2+4x-1<BR>\n" );
document.write( "a method requiring the quadratic formula and substitution is required  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225592 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=225592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well that's certainly not the easy way.<BR>\n" );
document.write( "You have two equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%5E2%2B4x-1 ALIGN=MIDDLE  ALT=\"y=3x%5E2%2B4x-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=-2x%2Bb ALIGN=MIDDLE  ALT=\"y=-2x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Look for the intersection point.<BR>\n" );
document.write( "Set them equal to each other. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B4x-1=-2x%2Bb ALIGN=MIDDLE  ALT=\"3x%5E2%2B4x-1=-2x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B6x-%281%2Bb%29=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B6x-%281%2Bb%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the line is a tangent point, the curves only intersect at one point. <BR>\n" );
document.write( "Then x must be a double root and the equation must be a perfect square.<BR>\n" );
document.write( "Complete the square to solve for both x and b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2%2B2x%29-%281%2Bb%29=0 ALIGN=MIDDLE  ALT=\"3%28x%5E2%2B2x%29-%281%2Bb%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2%2B2x%2B1%29-%281%2Bb%29=3 ALIGN=MIDDLE  ALT=\"3%28x%5E2%2B2x%2B1%29-%281%2Bb%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B1%29%5E2=1%2Bb%2B3 ALIGN=MIDDLE  ALT=\"3%28x%2B1%29%5E2=1%2Bb%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B1%29%5E2=b%2B4=0 ALIGN=MIDDLE  ALT=\"3%28x%2B1%29%5E2=b%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x coordinate for intersection is <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;\" ><BR>\n" );
document.write( "and also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-4 ALIGN=MIDDLE  ALT=\"b=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-2x-4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-2x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );