document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=460473>Question 460473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good moprning everyone,<BR>\n" );
document.write( "This is my question:<BR>\n" );
document.write( "How do you graph a parabola. How do you know if the parabola opens upward or downward.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you<BR>\n" );
document.write( "Gina </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315832 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=315832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The 1st step would be to find the axis of symmetry.<BR>\n" );
document.write( "This would be a vertical line, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+x%5Bs%5D+ ALIGN=MIDDLE  ALT=\"+x+=+x%5Bs%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The parabola<BR>\n" );
document.write( "is symmetrical to the left and right of this line.<BR>\n" );
document.write( "If the equation is expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bs%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bs%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "The base, or the point with zero slope, will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bs%5D%2C+y%5Bs%5D+ ALIGN=MIDDLE  ALT=\"+x%5Bs%5D%2C+y%5Bs%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Plug the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bs%5D+ ALIGN=MIDDLE  ALT=\"+x%5Bs%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > back into the equation to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bs%5D+ ALIGN=MIDDLE  ALT=\"+y%5Bs%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive, the parabola opens up.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, it opens down.<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Here's an example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2x%5E2+%2B+3x+-+12+ ALIGN=MIDDLE  ALT=\"+y+=+-2x%5E2+%2B+3x+-+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, so it opens down.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bs%5D+=+%28-3%29%2F%282%2A%28-2%29%29+ ALIGN=MIDDLE  ALT=\"+x%5Bs%5D+=+%28-3%29%2F%282%2A%28-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bs%5D+=+3%2F4+ ALIGN=MIDDLE  ALT=\"+x%5Bs%5D+=+3%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the axis of symmetry<BR>\n" );
document.write( "Plugging this back in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2%2A%283%2F4%29%5E2+%2B+3%2A%283%2F4%29+-+12+ ALIGN=MIDDLE  ALT=\"+y+=+-2%2A%283%2F4%29%5E2+%2B+3%2A%283%2F4%29+-+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-9%2F8+%2B+18%2F8+-+96%2F8+ ALIGN=MIDDLE  ALT=\"+y+=+-9%2F8+%2B+18%2F8+-+96%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-88%2F8+ ALIGN=MIDDLE  ALT=\"+y+=+-88%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bs%5D+=+-11+ ALIGN=MIDDLE  ALT=\"+y%5Bs%5D+=+-11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the base point is (3/4, -11)<BR>\n" );
document.write( "The parabola can touch the x-axis in<BR>\n" );
document.write( "1 point, 2 points, or no points.<BR>\n" );
document.write( "Here's a plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+5%2C+-25%2C+5%2C+-2x%5E2+%2B+3x+-+12+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+5%2C+-25%2C+5%2C+-2x%5E2+%2B+3x+-+12+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y-intercept is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0+ ALIGN=MIDDLE  ALT=\"+x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2%2A%280%29%5E2+%2B+3%2A%280%29+-+12+ ALIGN=MIDDLE  ALT=\"+y+=+-2%2A%280%29%5E2+%2B+3%2A%280%29+-+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-12+ ALIGN=MIDDLE  ALT=\"+y+=+-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so you have the point (0, -12) </SPAN>\n" );
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