document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133422>Question 133422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> when plotting y=x^2-4x+3 i first found the values for when x is 0 and when y is 0, but how do you determine if its above the x axis and if its a maximum or a minimum?<BR>\n" );
document.write( "Thanks<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 #97595 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=97595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can tell whether a parabola opens 'up' or 'down' by the sign on the high order term. In this case that term is <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;\" >. Since the sign is positive, the parabola opens 'up'.\r<BR>\n" );
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document.write( "To determine if the entire parabola lies above the x axis, you can set y = 0 and then solve for x. If there is no value of x that allows a y =0, then the entire parabola is above the x axis. If there is a single value of x that makes y=0, then the parabola \"just touches\" the x axis. If there are 2 values that make y=0, then the parabola crosses the x axis and has at least some part of below the x axis. \r<BR>\n" );
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document.write( "That is the case here:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-4x+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-4x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x-3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"y+=+%28x-3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Setting y =0 and solving for x yields values of x at 1 and 3 that allow y to be 0. --> two x values imply some part is below \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28600%2C400%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-4x%2B3+%29+ ALIGN=MIDDLE  ALT=\"graph+%28600%2C400%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-4x%2B3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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