document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195118>Question 195118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9.) Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. <BR>\n" );
document.write( "y = 2x2 + x + 3 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10.) Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. <BR>\n" );
document.write( "y = 3x2 - 12x + 12 <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146615 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=146615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%28x%5E2%2B1%2F2x%29%2B3 ALIGN=MIDDLE  ALT=\"y=2%28x%5E2%2B1%2F2x%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%28x%5E2%2B1%2F2x%2B1%2F16%29-1%2F8%2B3 ALIGN=MIDDLE  ALT=\"y=2%28x%5E2%2B1%2F2x%2B1%2F16%29-1%2F8%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%28x%2B1%2F4%29%5E2%2B23%2F8 ALIGN=MIDDLE  ALT=\"y=2%28x%2B1%2F4%29%5E2%2B23%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "equation with the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2 ALIGN=MIDDLE  ALT=\"y=ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >open up or down....if a postive it opens up and if a is negative opens down<BR>\n" );
document.write( ":<BR>\n" );
document.write( "since the vertex is at (-1/4,23,8) and lies above the x axis and a is positive meaning this parabola opens up then we know it doesnt cross the x axis.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%5E2%2Bx%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%5E2%2Bx%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "10) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%28x%5E2-4x%2B4%29-12%2B12 ALIGN=MIDDLE  ALT=\"y=3%28x%5E2-4x%2B4%29-12%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"y=3%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "since the vertex is at (2,0) and lies on x axis and a is positive meaning this parabola opens up then we know has only one point in common with the x axis and that point is (2,0)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%5E2-12x%2B12%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%5E2-12x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );