document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=439903>Question 439903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please I need some extra help with this problems!!<BR>\n" );
document.write( " Graphing Parabolas, for example this y= -x^2-2x+1?\r<BR>\n" );
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document.write( "please explain me how you do it?\r<BR>\n" );
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document.write( "   Thanks, Brian<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 #304010 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=304010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graphing the parabola:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    1.    Determine whether the parabola opens <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=upward ALIGN=MIDDLE  ALT=\"upward\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=downward ALIGN=MIDDLE  ALT=\"downward\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "            a.    If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3E+0 ALIGN=MIDDLE  ALT=\"a+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it opens <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=upward ALIGN=MIDDLE  ALT=\"upward\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "            b.    If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+0 ALIGN=MIDDLE  ALT=\"a+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it opens <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=downward ALIGN=MIDDLE  ALT=\"downward\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "    2.    Determine the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "            a.    The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-coordinate ALIGN=MIDDLE  ALT=\"x-coordinate\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "            b.    The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-coordinate ALIGN=MIDDLE  ALT=\"y-coordinate\"   DISABLED_style= \"max-width:90%; height:auto;\" > is found by substituting the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-coordinate ALIGN=MIDDLE  ALT=\"x-coordinate\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "    3.    Determine the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-intercept+ ALIGN=MIDDLE  ALT=\"y-intercept+\"   DISABLED_style= \"max-width:90%; height:auto;\" >by setting <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;\" >.\r<BR>\n" );
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document.write( "    4.    Determine the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" > (if any) by setting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,or solving the equation<BR>\n" );
document.write( "          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "    5.    Determine two or three other points if there are no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ".example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-x%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"y=+-x%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+0 ALIGN=MIDDLE  ALT=\"a+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it opens <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=downward ALIGN=MIDDLE  ALT=\"downward\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "a.    The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-coordinate ALIGN=MIDDLE  ALT=\"x-coordinate\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a=-%28-2%29%2F2%28-1%29=2%2F-2=-1 ALIGN=MIDDLE  ALT=\"-b%2F2a=-%28-2%29%2F2%28-1%29=2%2F-2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. substitute the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-coordinate ALIGN=MIDDLE  ALT=\"x-coordinate\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-x%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"y=+-x%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-%28-1%29%5E2-2%28-1%29%2B1 ALIGN=MIDDLE  ALT=\"y=+-%28-1%29%5E2-2%28-1%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-1%2B2%2B1 ALIGN=MIDDLE  ALT=\"y=+-1%2B2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+2 ALIGN=MIDDLE  ALT=\"y=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   DISABLED_style= \"max-width:90%; height:auto;\" > is at (-1,2)\r<BR>\n" );
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document.write( " 3.    Determine the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-intercept+ ALIGN=MIDDLE  ALT=\"y-intercept+\"   DISABLED_style= \"max-width:90%; height:auto;\" >by setting <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;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-%280%29%5E2-2%280%29%2B1 ALIGN=MIDDLE  ALT=\"y=+-%280%29%5E2-2%280%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.    Determine the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" > (if any) by setting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,or solving the equation<BR>\n" );
document.write( "      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-x%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"y=+-x%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-x%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"0=+-x%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-2%29+%2B-+sqrt%28%28-2%29%5E2-4%2A%28-1%29%2A1+%29%29%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-2%29+%2B-+sqrt%28%28-2%29%5E2-4%2A%28-1%29%2A1+%29%29%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%284%2B4+%29%29%2F-2%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%284%2B4+%29%29%2F-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%288%29%29%2F-2%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%288%29%29%2F-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+2.83%29%2F-2+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+2.83%29%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B+2.83%29%2F-2+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B+2.83%29%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4.83%2F-2+ ALIGN=MIDDLE  ALT=\"x+=+4.83%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++-2.41+ ALIGN=MIDDLE  ALT=\"x+=++-2.41+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+-+2.83%29%2F-2+ ALIGN=MIDDLE  ALT=\"x+=+%282+-+2.83%29%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.83%2F-2+ ALIGN=MIDDLE  ALT=\"x+=+0.83%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++-0.41+ ALIGN=MIDDLE  ALT=\"x+=++-0.41+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " 5.    Determine two or three other points if there are no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you skip this step\r<BR>\n" );
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document.write( "let see the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-x%5E2-2x%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-x%5E2-2x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );