document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=453993>Question 453993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of a and b that make f continuous everywhere. <BR>\n" );
document.write( "f (x)= <BR>\n" );
document.write( "{ <BR>\n" );
document.write( "x2&#8722;4x&#8722;2 if x<2 <BR>\n" );
document.write( "ax2&#8722;bx+3 if 2&#8804;x<3 <BR>\n" );
document.write( "2x&#8722;a+b if x&#8805;3 }\r<BR>\n" );
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document.write( "I dont understand how i would solve this. Please help. Thank you. :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #311808 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=311808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the values of a and b that make f continuous everywhere. <BR>\n" );
document.write( "f (x)= <BR>\n" );
document.write( "{ <BR>\n" );
document.write( "1. x^2&#8722;4x&#8722;2 if x<2 <BR>\n" );
document.write( "2. ax2&#8722;bx+3 if 2&#8804;x<3 <BR>\n" );
document.write( "3. 2x&#8722;a+b if x&#8805;3 } <BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Evaluate \"1\" at x = 2<BR>\n" );
document.write( "f(2) = 2^2-4*2-2 = -6<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Evaluate \"3\" at x = 3<BR>\n" );
document.write( "g(3) = 2(3)-a+b = 6-a+b<BR>\n" );
document.write( "----<BR>\n" );
document.write( "So two of the points of \"2\" must be (2,-6) and (3,6-a+b)<BR>\n" );
document.write( "____<BR>\n" );
document.write( "Substitute those coordinates into \"2\"<BR>\n" );
document.write( "to solve for \"a\" and for \"b\".<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2. ax2&#8722;bx+3<BR>\n" );
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document.write( "(2,-6) gives you 4a-2b+3 = -6<BR>\n" );
document.write( "2a - b = -9<BR>\n" );
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document.write( "(3,6-a+b) gives you a(9)-b(3)+3 = 6-a+b<BR>\n" );
document.write( "10a - 4b = 3<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Solve the system:<BR>\n" );
document.write( "2a - b = -9<BR>\n" );
document.write( "10a -4b = 3<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Multiply thru 1st equation by 5:<BR>\n" );
document.write( "10a - 5b = -45<BR>\n" );
document.write( "10a - 4b =  3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Subtract to get:<BR>\n" );
document.write( "b = 48<BR>\n" );
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document.write( "Solve for \"a\":<BR>\n" );
document.write( "2a - b = -9<BR>\n" );
document.write( "2a - 48 = -9<BR>\n" );
document.write( "2a = 39<BR>\n" );
document.write( "a = 39/2<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "I'd suggest you check alll the arithmetic<BR>\n" );
document.write( "here as mistakes can creep in.<BR>\n" );
document.write( "======================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );