document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=20187>Question 20187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph (Show your work)<BR>\n" );
document.write( "y=16-x^2<BR>\n" );
document.write( "Thanks a bunch </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9736 by </B><A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><B>mmm4444bot(95)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><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=9736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello There:\r<BR>\n" );
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document.write( "First of all, you should recognize the expression on the right side of the equals sign to be a quadratic expression.  In other words, it's in the form of:\r<BR>\n" );
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document.write( "y = a*x^2 + b*x + c\r<BR>\n" );
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document.write( "Hopefully you know that the graph is going to be a parabola.\r<BR>\n" );
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document.write( "We have:\r<BR>\n" );
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document.write( "y = -x^2 + 16\r<BR>\n" );
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document.write( "Right away, we see that the parabola opens downward because the value of \"a\" is negative.\r<BR>\n" );
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document.write( "There are formulas for the x- and y-coordinates of the vertex point.\r<BR>\n" );
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document.write( "x-coordinate = -b/(2*a)\r<BR>\n" );
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document.write( "y-coordinate = c - b^2/(4*a)\r<BR>\n" );
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document.write( "Our equation shows that:\r<BR>\n" );
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document.write( "a = -1\r<BR>\n" );
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document.write( "b = 0\r<BR>\n" );
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document.write( "c = 16\r<BR>\n" );
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document.write( "Substitute these values into the formula above to find that (0, 16) is the vertex point.\r<BR>\n" );
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document.write( "The expression 16 - x^2 can be factored as a difference of squares.\r<BR>\n" );
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document.write( "(4 + x)*(4 - x)=0\r<BR>\n" );
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document.write( "So, the x-intercepts of the graph are (-4, 0) and (4, 0).\r<BR>\n" );
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document.write( "Pick some other values of x, and find the corresponding values of y to get a few more points to plot.  Then draw the parabola using a smooth curve that goes through all of the points that you have plotted.\r<BR>\n" );
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document.write( "~ Mark<BR>\n" );
document.write( " </SPAN>\n" );
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