document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82935>Question 82935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Plot each pair of equations, then what is their intersection points?<BR>\n" );
document.write( "y1=x^2-1<BR>\n" );
document.write( "Y2=-1\r<BR>\n" );
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document.write( "I did <BR>\n" );
document.write( "  x^2-1=-1<BR>\n" );
document.write( "= x^2-1=1=0<BR>\n" );
document.write( "= x^2=0<BR>\n" );
document.write( "= x=0\r<BR>\n" );
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document.write( "But I don't know how to plot them.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59525 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=59525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I did <BR>\n" );
document.write( "  x^2-1=-1  <=== Good. You did this by setting Y1 equal to Y2<BR>\n" );
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document.write( "x^2-1=1=0 <=== A little confusing here. What you need to do is to get the x^2 term by itself <BR>\n" );
document.write( "on the left side. To do that you eliminate the -1 on the left side by adding +1 to both sides.<BR>\n" );
document.write( "When you do that you get the next equation that you got. <BR>\n" );
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document.write( "x^2=0  <=== This is correct.<BR>\n" );
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document.write( "x=0   <=== This is also correct. It tells you that when x equals zero, the two equations<BR>\n" );
document.write( "you originally were given have equal values of y.  Return to the original equations <BR>\n" );
document.write( "and substitute zero for x and you get:<BR>\n" );
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document.write( "Y1 = x^2 - 1<BR>\n" );
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document.write( "Then substituting zero for x results in:<BR>\n" );
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document.write( "Y1 = 0 -1 = -1<BR>\n" );
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document.write( "The second equation that you were given was:<BR>\n" );
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document.write( "Y2 = -1<BR>\n" );
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document.write( "Since this equation does not contain an x term, Y2 is -1 no matter what value is assigned<BR>\n" );
document.write( "to x.<BR>\n" );
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document.write( "From the first equation you know that (0, -1) is the point that has a Y value of -1. And<BR>\n" );
document.write( "from the second equation you know that (0, -1) is also a point that is common with the<BR>\n" );
document.write( "solution of the first equation.<BR>\n" );
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document.write( "What this all means is that (0, -1) is the point that these two equations have in common.<BR>\n" );
document.write( "And what is going on is that the graph of the first equation is a parabola that as you move<BR>\n" );
document.write( "to the right drops down to its minimum value of -1 [at the point (0, -1)] and then as<BR>\n" );
document.write( "you continue to move to the right rises. The Y axis is the line about which this parabola<BR>\n" );
document.write( "is symmetrically centered.<BR>\n" );
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document.write( "In the meantime the line Y2 = -1 is a horizontal line that is tangent to the bottom of<BR>\n" );
document.write( "the parabola of the first equation at the point (0, -1). So there is only one point of<BR>\n" );
document.write( "intersection ... and that is the point (0, -1).  The coordinate system below shows the<BR>\n" );
document.write( "graphs you should have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+x%5E2-1%2C-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+x%5E2-1%2C-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps to clarify the points you were looking for.<BR>\n" );
document.write( ".\r<BR>\n" );
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