document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116122>Question 116122</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131492624/algebrahomeworkh>Introductury Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please can you help me with this equation, I've been working it out but I'm not able to get the right answer. Graph and solve the equation.\r<BR>\n" );
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document.write( "y= x^2 - 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84430 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=84430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sometimes it's easier to just do a little analysis and not get lost in math. Let's try that <BR>\n" );
document.write( "approach.<BR>\n" );
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document.write( "First, the right side of the equation is a quadratic form (the highest power of x is the 2nd <BR>\n" );
document.write( "power). From that you know that the graph will be a parabola. And since the sign on the<BR>\n" );
document.write( "x-squared term is positive, you can tell that as you move from the left to the right along<BR>\n" );
document.write( "the x-axis the graph will drop more and more until it reaches some low point, and then it will<BR>\n" );
document.write( "start to rise more and more as you move further to the right. You also know that if you draw<BR>\n" );
document.write( "a vertical line through that low point on the graph the graph to the left of that line will<BR>\n" );
document.write( "look like the mirror image of the graph to the right of that line.<BR>\n" );
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document.write( "[For your information in other problems of this type, if the sign on the x-squared term<BR>\n" );
document.write( "is negative, you can tell that the graph will rise to a peak and then fall back down<BR>\n" );
document.write( "the further you go to the right along the x-axis.]<BR>\n" );
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document.write( "Now you can just calculate some points to help you understand what the graph looks like.<BR>\n" );
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document.write( "One nice and easy point on the graph can be found by setting x equal to zero and finding what<BR>\n" );
document.write( "the corresponding value of y is. When you set x equal to zero in the given equation for<BR>\n" );
document.write( "y, you get:<BR>\n" );
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document.write( "y = (0)^2 - 4 = -4<BR>\n" );
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document.write( "Now you know that the point (0, -4) is on the graph. Plot it.<BR>\n" );
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document.write( "Next let's try letting x = +1 and calculate y. Substituting x into the given equation<BR>\n" );
document.write( "results in:<BR>\n" );
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document.write( "y = (1)^2 - 4 = 1 - 4 = -3<BR>\n" );
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document.write( "This time you know that the point (1, -3) is on the graph<BR>\n" );
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document.write( "Next let's set x equal to -1 and calculate the corresponding value of y.<BR>\n" );
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document.write( "y = (-1)^2 - 4 = 1 - 4 = -3<BR>\n" );
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document.write( "Now you know that (-1, -3) is on the graph.<BR>\n" );
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document.write( "Now let's set x = 2 to find that:<BR>\n" );
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document.write( "y = (2)^2 - 4 = 4 - 4 = 0<BR>\n" );
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document.write( "This time you know that (2, 0) is on the graph. Then if you set x = -2 you get the corresponding<BR>\n" );
document.write( "value of y to be:<BR>\n" );
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document.write( "y = (-2)^2 - 4 = +4 - 4 = 0<BR>\n" );
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document.write( "The point (-2, 0) is on the graph.<BR>\n" );
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document.write( "If you have plotted these five points on the graph you should have a pretty good idea of what<BR>\n" );
document.write( "the parabola looks like. You can use more values for x to find corresponding values of<BR>\n" );
document.write( "y and get more points on the graph. With more points you should find that it looks like:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+400%2C+400%2C+-10%2C10%2C-5%2C+15%2C+x%5E2+-+4%29 ALIGN=MIDDLE  ALT=\"graph%28+400%2C+400%2C+-10%2C10%2C-5%2C+15%2C+x%5E2+-+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you are to \"solve\" this equation that means that you are looking for the value of x<BR>\n" );
document.write( "where the graph crosses the x-axis. If you've done your graphing pretty accurately<BR>\n" );
document.write( "you should see that the graph crosses the x-axis at two places ... where x = -2 and x = +2.<BR>\n" );
document.write( "This means that for those two values of x the corresponding value of y is zero.<BR>\n" );
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document.write( "Hope this helps you with a little different slant on this problem.<BR>\n" );
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