document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085857>Question 1085857</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the x-intercepts of the parabola with vertex (-3,16) and y-intercept (0,-20). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699955 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=699955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general formula 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 formula for the vertex is:<BR>\n" );
document.write( "<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( "---------------------------<BR>\n" );
document.write( "You are given 2 points:<BR>\n" );
document.write( "( -3,16 )<BR>\n" );
document.write( "( 0, -20 )<BR>\n" );
document.write( "Plug these values into the general formula<BR>\n" );
document.write( "(-3,16)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+=+a%2A%28-3%29%5E2+%2B+b%2A%28-3%29+%2B+c+ ALIGN=MIDDLE  ALT=\"+16+=+a%2A%28-3%29%5E2+%2B+b%2A%28-3%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=+9a+-+3b+%2B+c+=+16+ ALIGN=MIDDLE  ALT=\"+9a+-+3b+%2B+c+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(0,-20)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-20+=+a%2A0%5E2+%2B+b%2A0+%2B+c+ ALIGN=MIDDLE  ALT=\"+-20+=+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=+c+=+-20+ ALIGN=MIDDLE  ALT=\"+c+=+-20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Now the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+-+20+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Al;so:<BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-3+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( given )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-3+=+-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+=+-6a+ ALIGN=MIDDLE  ALT=\"+-b+=+-6a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+6a+ ALIGN=MIDDLE  ALT=\"+b+=+6a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, now I have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+%286a%29%2Ax+-+20+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+%286a%29%2Ax+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "also<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bv%5D+=+16+ ALIGN=MIDDLE  ALT=\"+y%5Bv%5D+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( given )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+=+a%2A%28-3%29%5E2+%2B+%286a%29%2A%28-3%29+-+20+ ALIGN=MIDDLE  ALT=\"+16+=+a%2A%28-3%29%5E2+%2B+%286a%29%2A%28-3%29+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+=+9a+-+18a+-+20+ ALIGN=MIDDLE  ALT=\"+16+=+9a+-+18a+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9a+=+36+ ALIGN=MIDDLE  ALT=\"+-9a+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-4+ ALIGN=MIDDLE  ALT=\"+a+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+6a+ ALIGN=MIDDLE  ALT=\"+b+=+6a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-24+ ALIGN=MIDDLE  ALT=\"+b+=+-24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-4x%5E2+-+24x+-+20+ ALIGN=MIDDLE  ALT=\"+y+=+-4x%5E2+-+24x+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Find the roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-24%29+%2B+sqrt%28+%28-24%29%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-24%29+%2B+sqrt%28+%28-24%29%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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%5B1%5D+=+%28+24+%2B+sqrt%28+576+-+4%2A%28-4%29%2A%28-20%29+%29%29%2F%282%2A%28-4%29%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28+24+%2B+sqrt%28+576+-+4%2A%28-4%29%2A%28-20%29+%29%29%2F%282%2A%28-4%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%5B1%5D+=+%28+24+%2B+sqrt%28+576+-+320+%29%29%2F%28-8%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28+24+%2B+sqrt%28+576+-+320+%29%29%2F%28-8%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%5B1%5D+=+%28+24+%2B+sqrt%28+256+%29%29%2F%28-8%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28+24+%2B+sqrt%28+256+%29%29%2F%28-8%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%5B1%5D+=+%28+24+%2B+16+%29%2F%28-8%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28+24+%2B+16+%29%2F%28-8%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%5B1%5D+=+40%2F%28-8%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+40%2F%28-8%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%5B1%5D+=+-5+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The other root is at:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B2%5D+=+%28+24+-+16+%29%2F%28-8%29+ ALIGN=MIDDLE  ALT=\"+x%5B2%5D+=+%28+24+-+16+%29%2F%28-8%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%5B2%5D+=+8%2F%28-8%29+ ALIGN=MIDDLE  ALT=\"+x%5B2%5D+=+8%2F%28-8%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%5B2%5D+=+-1+ ALIGN=MIDDLE  ALT=\"+x%5B2%5D+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x-intercepts are:<BR>\n" );
document.write( "( -5,0 ) and ( -1,0 )<BR>\n" );
document.write( "-----------------------<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+-10%2C+2%2C+-5%2C+20%2C+-4x%5E2+-+24x+-+20+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+2%2C+-5%2C+20%2C+-4x%5E2+-+24x+-+20+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "check the math and get an other opinion if needed\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );