document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32006>Question 32006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the graph of each parabola opens upward or downward.\r<BR>\n" );
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document.write( "y= -1/2^x^2+3\r<BR>\n" );
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document.write( "Please help me to understand what parabola means.\r<BR>\n" );
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document.write( "Textbook Elementary and Intermediate Algebra. Mark Dugopolski\r<BR>\n" );
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document.write( "ISBN: 13978-0-07-326862-0<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 #18529 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=18529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A parabola is one of the \"conic sections\", so-called beacause it's one of the curves you get when you slice a right-circular cone in one of several ways.<BR>\n" );
document.write( "The other conic sections are:<BR>\n" );
document.write( "The circle, the ellipse, and the hyperbola.\r<BR>\n" );
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document.write( "You can \"see\" the parabola when you graph a quadratic equation.<BR>\n" );
document.write( "You can tell which way the parabola opens from the sign of the coefficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-term.\r<BR>\n" );
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document.write( "If this coefficient is positive, the parabola opens upward.<BR>\n" );
document.write( "If this coefficient is negative, the parabola opens downward.\r<BR>\n" );
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document.write( "In your problem, the quadratic equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%5E2+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%5E2+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you can see that the coefficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, so the parabola opens downward.\r<BR>\n" );
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document.write( "Here's the graph of your equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C-%281%2F2%29x%5E2%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C-%281%2F2%29x%5E2%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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