document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703933>Question 703933</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the parabola when the x intercept is -6, y intercept is 36 and axis of symmetry is x=-6.\r<BR>\n" );
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document.write( "Can you please help me? Thanks so much in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433834 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=433834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The only way that both the x-intercept and<BR>\n" );
document.write( "the axis of symmetry can <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+6+ ALIGN=MIDDLE  ALT=\"+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is if the <BR>\n" );
document.write( "parabola just touches the x-axis and thus<BR>\n" );
document.write( "only has 1 solution- called a double root.<BR>\n" );
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document.write( "If the y intercept is positive, that tells me <BR>\n" );
document.write( "the parabola has a minimum and not a maximum.<BR>\n" );
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document.write( "If the form is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The roots ( x-intercepts ) are given by:<BR>\n" );
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;\" > <BR>\n" );
document.write( "When there is a double root, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+=+4%2Aa%2Ac+ ALIGN=MIDDLE  ALT=\"+b%5E2+=+4%2Aa%2Ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+b%5E2%2F%284c%29+ ALIGN=MIDDLE  ALT=\"+a+=+b%5E2%2F%284c%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The y-intercept occurs at ( 0,36 ), so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36+=+a%2A0+%2B+b%2A0+%2B+c+ ALIGN=MIDDLE  ALT=\"+36+=+a%2A0+%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=+c+=+36+ ALIGN=MIDDLE  ALT=\"+c+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The x-coordinate of the axis of symmetry is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-6+=+-b%2F%282a%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+=+12a+ ALIGN=MIDDLE  ALT=\"+b+=+12a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+12%2A%28+b%5E2+%2F+%28+4%2A36%29+%29+ ALIGN=MIDDLE  ALT=\"+b+=+12%2A%28+b%5E2+%2F+%28+4%2A36%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=+144b+=+12b%5E2+ ALIGN=MIDDLE  ALT=\"+144b+=+12b%5E2+\"   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( "and, since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+12a+ ALIGN=MIDDLE  ALT=\"+b+=+12a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+b%2F12+ ALIGN=MIDDLE  ALT=\"+a+=+b%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+12%2F12+ ALIGN=MIDDLE  ALT=\"+a+=+12%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "The equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%5E2+%2B+12x+%2B+36+ ALIGN=MIDDLE  ALT=\"+y+=+x%5E2+%2B+12x+%2B+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28+x+%2B+6+%29%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+%28+x+%2B+6+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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+-14%2C+2%2C+-2%2C+50%2C+%28+x+%2B+6+%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-14%2C+2%2C+-2%2C+50%2C+%28+x+%2B+6+%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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