document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=49123>Question 49123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> indicate whether the graphs of the following will have a maximum or a minimum.<BR>\n" );
document.write( "1. f(x)=x exponent 2-9\r<BR>\n" );
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document.write( "2.f(x)=8x-3x exponent 2\r<BR>\n" );
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document.write( "3.f(x)=-(3-x)exponent 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #32551 by </B><A HREF=/tutors/aboutme.mpl?userid=Born2TeachMath><B>Born2TeachMath(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Born2TeachMath><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=32551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your teacher is trying to get you to realize that the coefficient of the x^2 term in a quadratic graph determines whether the graph of a parabola will open up (and have a bottom - or minimum value) or open upside down (and have a top - or maximum value).\r<BR>\n" );
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document.write( "If the coefficient of the x^2 term is positive, then the graph of the parabola opens upwards, and will have a minimum value.\r<BR>\n" );
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document.write( "If the coefficient of the x^2 term is negative, then the graph of the parabola opens downward, and will have a maximum value.\r<BR>\n" );
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document.write( "The up or down direction does not depend on either the sign of the x-term or the constant at the end.  These two have other significance which you'll get into later, I'm sure. \r<BR>\n" );
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document.write( "So, to answer your questions:\r<BR>\n" );
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document.write( "1. f(x) = x^2 - 9 will open up and have a minimum, since the coefficient of the x^2 is +1.<BR>\n" );
document.write( "2. f(x) = 8x - 3x^2 will open down and have a maximum, since the coefficient of the x^2 is -3<BR>\n" );
document.write( "3. f(x)=-(3-x)^2\r<BR>\n" );
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document.write( "This one is a bit trickier.  You really should simplify the left side by multiplying it out:\r<BR>\n" );
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document.write( "-(3-x)^2 = -(3-x)(3-x)  definition of squaring = multiplying by itself<BR>\n" );
document.write( "= -(9-6x+x^2)  FOIL it out.<BR>\n" );
document.write( "=-9+6x-x^2  distribute the (-).\r<BR>\n" );
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document.write( "Therefore, the parabola will open down and have a maximum, since the coefficient of the x^2 is -1\r<BR>\n" );
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document.write( "Don't try to just guess on #3! </SPAN>\n" );
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