document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116777>Question 116777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the real roots of the equation by graphing: y=2x^2+2x-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84899 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=84899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "y = 2x^2 + 2x - 4<BR>\n" );
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document.write( "You can graph this equation by setting x equal to some value and then calculating the corresponding<BR>\n" );
document.write( "value of y. Then plot the point (x, y) for each calculation. <BR>\n" );
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document.write( "An easy one is to set x equal to zero. When you do, the equation reduces to:<BR>\n" );
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document.write( "y = 0 + 0 -4 = -4<BR>\n" );
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document.write( "So now you know that the point (0, -4) is on the graph. Plot it.<BR>\n" );
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document.write( "Next you might let x = +1. This makes the equation:<BR>\n" );
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document.write( "y = 2 + 2 - 4 = 0<BR>\n" );
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document.write( "This means the point (1, 0) is on the graph. Keep doing this for convenient values of x,<BR>\n" );
document.write( "both positive values and negative values. (The more (x, y) points you get, the more you will<BR>\n" );
document.write( "be able to pinpoint the roots. <BR>\n" );
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document.write( "The roots you are looking for are the values of x where the graph intersects the x-axis. There<BR>\n" );
document.write( "are three possibilities ... the graph will cut across the x-axis at two points meaning that<BR>\n" );
document.write( "there are two real roots. Or the graph will just touch or be tangent to the x-axis meaning<BR>\n" );
document.write( "that there is only one real root. Or the graph will not touch or cut across the x-axis meaning<BR>\n" );
document.write( "that there are no real roots.<BR>\n" );
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document.write( "When you graph the given equation y = 2x^2 + 2x - 4 the graph will look like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-10%2C10%2C-10%2C10%2C2x%5E2+%2B+2x+-4%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C800%2C-10%2C10%2C-10%2C10%2C2x%5E2+%2B+2x+-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "From this graph it appears that the roots are x = -2 and x = +1. If these answers are<BR>\n" );
document.write( "correct you can plug them (one at a time) into the given equation for x and the corresponding<BR>\n" );
document.write( "value of y should turn out to be zero.<BR>\n" );
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document.write( "Hope this helps you to understand the problem, what it is asking you to do, and how you go <BR>\n" );
document.write( "about getting the answer.<BR>\n" );
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