document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=532379>Question 532379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x)=x^2-3 and f(a)=46, what is the value of a? Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350829 by </B><A HREF=/tutors/aboutme.mpl?userid=lmeeks54><B>lmeeks54(111)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lmeeks54><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=lmeeks54><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=350829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The only tricky thing here is to understand what is meant by f(a) = ?<BR>\n" );
document.write( "...<BR>\n" );
document.write( "This is basically just solving the quadratic equation.<BR>\n" );
document.write( "Given: <BR>\n" );
document.write( "f(x) = x^2 - 3<BR>\n" );
document.write( "f(a) = 46<BR>\n" );
document.write( "...<BR>\n" );
document.write( "In this case, f(a) means solving the f(x) equation as if a = x.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "So, f(x) = f(a)<BR>\n" );
document.write( "x^2 - 3 = 46<BR>\n" );
document.write( "...<BR>\n" );
document.write( "The easiest way to solve quadratic equations is to rearrange them (using the rules of algebra) so that the equation is set = 0<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Therefore, subtract 46 from both sides and simplify:<BR>\n" );
document.write( "x^2 - 3 - 46 = 46 - 46<BR>\n" );
document.write( "x^2 - 49 = 0<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Factor the quadratic equation:<BR>\n" );
document.write( "x^2 - 49 = 0 is factored to become:<BR>\n" );
document.write( "(x + 7)(x - 7) = 0<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Solving for x to satisfy the factored quadratic equation:<BR>\n" );
document.write( "x = 7, or -7<BR>\n" );
document.write( "...<BR>\n" );
document.write( "So, when f(a) = 46, a = 7 or -7<BR>\n" );
document.write( "...<BR>\n" );
document.write( "check the work:<BR>\n" );
document.write( "(7)^2 - 3 = 46<BR>\n" );
document.write( "49 - 3 = 46<BR>\n" );
document.write( "46 = 46 checks<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Note: if we substitute -7 into the function, we get the same answer.<BR>\n" );
document.write( "a = 7, -7<BR>\n" );
document.write( "...<BR>\n" );
document.write( "cheers,<BR>\n" );
document.write( "Lee </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );