document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=807833>Question 807833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In which direction does the parabola open that has a Vertex at (2, -5) and y-intercept at -17 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #486553 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=486553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would say that it opens down because the <BR>\n" );
document.write( "y-intercept is more negative than the <BR>\n" );
document.write( "y-coordinate of the vertex.<BR>\n" );
document.write( "I should be able to prove it<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "I'll say the parabola is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is at ( 2,-5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-b%29%2F%282a%29+=+2+ ALIGN=MIDDLE  ALT=\"+%28-b%29%2F%282a%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b+=+4a+ ALIGN=MIDDLE  ALT=\"+-b+=+4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4a+ ALIGN=MIDDLE  ALT=\"+b+=+-4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "I can also say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5+=+a%2A2%5E2+%2B+b%2A2+%2B+c+ ALIGN=MIDDLE  ALT=\"+-5+=+a%2A2%5E2+%2B+b%2A2+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5+=+4a+%2B+2b+%2B+c+ ALIGN=MIDDLE  ALT=\"+-5+=+4a+%2B+2b+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5+=+4a+%2B+2%2A%28-4a%29+%2B+c+ ALIGN=MIDDLE  ALT=\"+-5+=+4a+%2B+2%2A%28-4a%29+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+8a+-+4a+-+5+ ALIGN=MIDDLE  ALT=\"+c+=+8a+-+4a+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+4a+-+5+ ALIGN=MIDDLE  ALT=\"+c+=+4a+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "And also<BR>\n" );
document.write( "(0,-17)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-17+=+a%2A0%5E2+%2B+b%2A0+%2B+c+ ALIGN=MIDDLE  ALT=\"+-17+=+a%2A0%5E2+%2B+b%2A0+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-17+=+c+ ALIGN=MIDDLE  ALT=\"+-17+=+c+\"   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=+c+=+4a+-+5+ ALIGN=MIDDLE  ALT=\"+c+=+4a+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-17+=+4a+-+5+ ALIGN=MIDDLE  ALT=\"+-17+=+4a+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+=+-12+ ALIGN=MIDDLE  ALT=\"+4a+=+-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+=+-3+ ALIGN=MIDDLE  ALT=\"+a+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4a+ ALIGN=MIDDLE  ALT=\"+b+=+-4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4%2A%28-3%29+ ALIGN=MIDDLE  ALT=\"+b+=+-4%2A%28-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+12+ ALIGN=MIDDLE  ALT=\"+b+=+12+\"   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=+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c++ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+-3x%5E2+%2B+12x+-+17+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+-3x%5E2+%2B+12x+-+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Does it go through (2,-5) ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5+=+-3%2A2%5E2+%2B+12%2A2+-+17+ ALIGN=MIDDLE  ALT=\"+-5+=+-3%2A2%5E2+%2B+12%2A2+-+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5+=+-12+%2B+24+-+17+ ALIGN=MIDDLE  ALT=\"+-5+=+-12+%2B+24+-+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5+=+12+-+17+ ALIGN=MIDDLE  ALT=\"+-5+=+12+-+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5+=+-5+ ALIGN=MIDDLE  ALT=\"+-5+=+-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK <BR>\n" );
document.write( "here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-4%2C+6%2C+-20%2C+5%2C+-3x%5E2+%2B+12x+-+17+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-4%2C+6%2C+-20%2C+5%2C+-3x%5E2+%2B+12x+-+17+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );