document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196940>Question 1196940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find f(k - 1) when f(x) = 4x^2 - 3x + 4\r<BR>\n" );
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document.write( "Answer key provided, nothing I attempt so far step wise gets me to the correct answer however.\r<BR>\n" );
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document.write( "Answer key says the answer is: \"4k^2 - 11k + 11\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829986 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "f(x) = 4x^2 - 3x + 4<BR>\n" );
document.write( "f(<font color=red>x</font>) = 4(<font color=red>x</font>)^2 - 3(<font color=red>x</font>) + 4 ... highlight all the variables we're going to replace; note the use of parenthesis<BR>\n" );
document.write( "f(<font color=red>k-1</font>) = 4(<font color=red>k-1</font>)^2 - 3(<font color=red>k-1</font>) + 4 ... each <font color=red>x</font> replaced with <font color=red>k-1</font><BR>\n" );
document.write( "The use of color-coding is optional, but I find it helps to see the replacements much easier.\r<BR>\n" );
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document.write( "The task is to now expand and simplify<BR>\n" );
document.write( "f(k-1) = 4(k-1)^2 - 3(k-1) + 4<BR>\n" );
document.write( "f(k-1) = 4(k-1)(k-1) - 3(k-1) + 4<BR>\n" );
document.write( "f(k-1) = 4(k^2-2k+1) - 3(k-1) + 4<BR>\n" );
document.write( "f(k-1) = 4k^2-8k+4 - 3k+3 + 4<BR>\n" );
document.write( "f(k-1) = 4k^2-11k+11\r<BR>\n" );
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document.write( "Side note:<BR>\n" );
document.write( "Here's a common mistake I see many students doing<BR>\n" );
document.write( "f(x) = 4x^2 - 3x + 4<BR>\n" );
document.write( "f(k-1) = 4k-1^2 - 3k-1 + 4<BR>\n" );
document.write( "This is NOT correct because we didn't involve parenthesis around the k-1 terms on the right hand side<BR>\n" );
document.write( "The temptation may be to simply search-and-replace each x with k-1, but I would say it should be \"replace x with (k-1)\" to be more accurate.<BR>\n" );
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