document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703935>Question 703935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the parabola with vertex (-2,0) and y intercept 4.\r<BR>\n" );
document.write( "\n" );
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 #433794 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=433794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First write down the general form<BR>\n" );
document.write( "of a parabola, which 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( "When in this form, the x-coordinate of the vertex<BR>\n" );
document.write( "is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You are given that the vertex is at ( -2,0 ), so I can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-2+=+-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=+2+=+b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+2+=+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+=+4a+ ALIGN=MIDDLE  ALT=\"+b+=+4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "So far, I have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+4a%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+4a%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y-intercept occurs where <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+=+a%2A0+%2B+4a%2A0+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2A0+%2B+4a%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=+y+=+c+ ALIGN=MIDDLE  ALT=\"+y+=+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You are given that the y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4+ ALIGN=MIDDLE  ALT=\"+y+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+=+c+ ALIGN=MIDDLE  ALT=\"+4+=+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "So far, I have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+4a%2Ax+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+4a%2Ax+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I go back to the vertex at ( -2,0 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+a%2A%28-2%29%5E2+%2B+4%2A%28-2%29+%2B+4+ ALIGN=MIDDLE  ALT=\"+0+=+a%2A%28-2%29%5E2+%2B+4%2A%28-2%29+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+4a+-+8+%2B+4+ ALIGN=MIDDLE  ALT=\"+0+=+4a+-+8+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+=+8+-+4+ ALIGN=MIDDLE  ALT=\"+4a+=+8+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+=+4+ ALIGN=MIDDLE  ALT=\"+4a+=+4+\"   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( "Now I have all I need to write the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+1%2Ax%5E2+%2B+4%2A1%2Ax+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+1%2Ax%5E2+%2B+4%2A1%2Ax+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%5E2+%2B+4x+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+x%5E2+%2B+4x+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "Does it go through ( 0,4) ? ( the y-intercept )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%5E2+%2B+4x+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+x%5E2+%2B+4x+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+=+0%5E2+%2B+4%2A0+%2B+4+ ALIGN=MIDDLE  ALT=\"+4+=+0%5E2+%2B+4%2A0+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+=+4+ ALIGN=MIDDLE  ALT=\"+4+=+4+\"   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+-6%2C+6%2C+-6%2C+10%2C+x%5E2+%2B+4x+%2B+4+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+10%2C+x%5E2+%2B+4x+%2B+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );