document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134282>Question 1134282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can please somebody help me solve this with explanation for a 8th grader. Thank you.\r<BR>\n" );
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document.write( "x^2-4|x|+3=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751623 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=751623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 - 4|x| + 3 = 0\r<BR>\n" );
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document.write( "x is in between the absolute value signs.\r<BR>\n" );
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document.write( "that means that:\r<BR>\n" );
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document.write( "if x is positive, then |x| = x.\r<BR>\n" );
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document.write( "if x is negative, then |x| = -x\r<BR>\n" );
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document.write( "for example, if x is euqal to 5, the |5| = 5.\r<BR>\n" );
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document.write( "if x is eual to -5, then |-5| = - (-5) = 5.\r<BR>\n" );
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document.write( "the result is that the value of x is always positive.\r<BR>\n" );
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document.write( "you have two situations.\r<BR>\n" );
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document.write( "if x is positive, then x^2 - 4|x| + 3 = 0 becomes x^2 - 4x + 3 = 0\r<BR>\n" );
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document.write( "if x is negative, then x^2 - 4(-x) + 3 = 0 which becomes x^2 + 4x + 3 = 0\r<BR>\n" );
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document.write( "the first equation is x^2 - 4x + 3 = 0\r<BR>\n" );
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document.write( "factor this to get (x - 3) * (x - 1) = 0\r<BR>\n" );
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document.write( "the second equation is (x + 3) * (x + 1) = 0\r<BR>\n" );
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document.write( "the roots of the equation are x = -3, x = -1, x = 1, x = 3.\r<BR>\n" );
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document.write( "those are the values of the equation when y = 0.\r<BR>\n" );
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document.write( "if you want to graph this equation, you would look for the following intervals.\r<BR>\n" );
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document.write( "x < -3<BR>\n" );
document.write( "x > -3 and < -1<BR>\n" );
document.write( "x > -1 and < 1<BR>\n" );
document.write( "x > 1 and < 3<BR>\n" );
document.write( "x > 3\r<BR>\n" );
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document.write( "you would then evaluate the equation in each of those intervals to see if it is greater than 0 or less than 0.\r<BR>\n" );
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document.write( "when x = -4, y = x^2 - 4|x| + 3 gets you y = 3 which is positive.<BR>\n" );
document.write( "when x = -2, y = x^2 - 4|x| + 3 gets you y = -1 which is negative.<BR>\n" );
document.write( "when x = 0, y = x^2 - 4|x| + 3 gets you y = 3 which is positive.<BR>\n" );
document.write( "when x = 2, y = x^2 - 4|x| + 3 gets you y = -1 which is negative.<BR>\n" );
document.write( "when x = 4, y = x^2 - 4|x| + 3 gets you y = 3 which is positive.\r<BR>\n" );
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document.write( "you can now draw a rough sketch of your graph.\r<BR>\n" );
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document.write( "i did the same but used graphing software found at desmos.com.\r<BR>\n" );
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document.write( "here's what the graph looks like with the zero points being shown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/020701.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here's what the graph looks like with the test points being shown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/020701.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "basically you're solving this the same way you solve any other absolute value problem.\r<BR>\n" );
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document.write( "you have to divide the function into two parts.\r<BR>\n" );
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document.write( "the first part is when the expression in the absolute value sign is positive.\r<BR>\n" );
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document.write( "the second part is when the expression in the absolute value sign is negative.\r<BR>\n" );
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document.write( "then solve each part separately. </SPAN>\n" );
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