document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=244895>Question 244895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello<BR>\n" );
document.write( "I have a function f(x) represented graphically, but the function f(x) is unknown. All i know is several values of f(x) at the corresponding x. How can i identify the expression of the function? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179039 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> graph the points and see what they look like.\r<BR>\n" );
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document.write( "if they look like a straight line, then your equation will be of the form:\r<BR>\n" );
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document.write( "ax + by = c\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "y = mx + b\r<BR>\n" );
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document.write( "if they look like a parabola (shaped like a u or an upside down u), then your equation will be of the form:\r<BR>\n" );
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document.write( "ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "(x-h)^2 + k = 0\r<BR>\n" );
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document.write( "the equation depends on the shape of the graph.  \r<BR>\n" );
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document.write( "that's a starting point.\r<BR>\n" );
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document.write( "from there you work back.\r<BR>\n" );
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document.write( "with a quadratic equation, you find the 0 points and solve backwards.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "when y = 0, x = 3 and x = -2\r<BR>\n" );
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document.write( "you have x = 3 and x = -2 which leads to the equation (x-3) * (x+3) = 0\r<BR>\n" );
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document.write( "you multiply those factors together and you have the quadratic equation.\r<BR>\n" );
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document.write( "this is exactly the reverse of how your would solve the quadratic equation to get the roots in the first place.\r<BR>\n" );
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document.write( "if you're still having trouble, send me the points and i'll take a look at it.\r<BR>\n" );
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