document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=421872>Question 421872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to solve this problem  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=x%5E2+-+4x+%2B+3 ALIGN=MIDDLE  ALT=\"y%5E2+=x%5E2+-+4x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #294529 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=294529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y^2 = x^2 - 4x + 3\r<BR>\n" );
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document.write( "set y^2 = 0 and you get:\r<BR>\n" );
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document.write( "x^2 - 4x + 3 = 0 which leads to (x-1)*(x-3) = 0 which leads to x = 1 and x = 3.\r<BR>\n" );
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document.write( "these are the roots of the quadratic equation.\r<BR>\n" );
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document.write( "a graph of that equation is shown below:\r<BR>\n" );
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document.write( "this, however, is the graph of y = ....., not y^2 = .....\r<BR>\n" );
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document.write( "the graph of y^2 = x^2 - 4x + 3 is shown below:\r<BR>\n" );
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document.write( "I'm just guessing because I've never seen a problem such as this before, but it appears that the roots are the same, except the graph of the equation is different.\r<BR>\n" );
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document.write( "this stands to reason because the equations are different after you solve for y.\r<BR>\n" );
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document.write( "y = x^2 - 4x + 3\r<BR>\n" );
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document.write( "versus\r<BR>\n" );
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document.write( "y = +/- sqrt(x^2 - 4x + 3)\r<BR>\n" );
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document.write( "in both cases, x is the independent variable and y is the dependent.\r<BR>\n" );
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document.write( "you select values of x for plotting your graph and then you calculate what the value of y would be for those values of x based on the equation.\r<BR>\n" );
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document.write( "in the equation of y^2 = x^2 - 4x + 3, the zone between x = 1 and x = 3 does not show on the graph most likely because the value of y is equal to the square root of a negative number which is not real, therefore can't be graphed on a graph that is dealing with real numbers only.\r<BR>\n" );
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document.write( "for example, when x = 2, y^2 = x^2 - 4x + 3 becomes 4 - 8 + 3 = -4 + 3 = -1\r<BR>\n" );
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document.write( "y = +/- sqrt(-1) is not a real number, therefore can't be graphed.\r<BR>\n" );
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document.write( "does this answer your question or were you looking for something else?\r<BR>\n" );
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