document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=453097>Question 453097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you know if the parabola opens upward or downward? What are 3 key points you can determine and graph from the equation? Demonstrate with an example.\r<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 #311314 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=311314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  How do you know if the parabola opens upward or downward? What are 3 key points you can determine and graph from the equation? Demonstrate with an example. \r<BR>\n" );
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document.write( "y = ax^2+bx+c<BR>\n" );
document.write( "If \"a\" is positive, opens upward.<BR>\n" );
document.write( "If \"a\" is negative, opens downward.<BR>\n" );
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document.write( "3 key points:<BR>\n" );
document.write( "2 x-intercepts or roots<BR>\n" );
document.write( "1 y-intercept<BR>\n" );
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document.write( "Example:<BR>\n" );
document.write( "x intercepts: (2,0) and (5,0)<BR>\n" );
document.write( "y intercept: (0,8)<BR>\n" );
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document.write( "y = ax^2 + bx + c<BR>\n" );
document.write( "Using (0,8) you know c = 8<BR>\n" );
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document.write( "Using the x-intercepts:<BR>\n" );
document.write( "0 = (x-2)(x-3)<BR>\n" );
document.write( "0 = x^2-5x+6<BR>\n" );
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document.write( "y = a(x^2-5x+6)<BR>\n" );
document.write( "y = ax^2-5ax+6a<BR>\n" );
document.write( "6a = 8<BR>\n" );
document.write( "a = 4/3<BR>\n" );
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document.write( "y = (4/3)x^2-(20/3)x+ (4/3)*6<BR>\n" );
document.write( "y = (4/3)x^2-(20/3)x + 8<BR>\n" );
document.write( "=====================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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