document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148201>Question 1148201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i make a quadratic equation from vertex point (4,-3) and point (6,-1)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769559 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=769559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form is <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 y-component of ( 6, -1 ) is greater than the<BR>\n" );
document.write( "y-component of the vertex, so I know the vertex is <BR>\n" );
document.write( "a minimum ( just an observation )<BR>\n" );
document.write( "----------------------------------------------------<BR>\n" );
document.write( "( 4, -3 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3+=+a%2A4%5E2+%2B+b%2A4+%2B+c+ ALIGN=MIDDLE  ALT=\"+-3+=+a%2A4%5E2+%2B+b%2A4+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3+=+16a+%2B+4b+%2B+c+ ALIGN=MIDDLE  ALT=\"+-3+=+16a+%2B+4b+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "For the vertex:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+4+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-8a+ ALIGN=MIDDLE  ALT=\"+b+=+-8a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "( 6, -1 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1+=+a%2A6%5E2+%2B+b%2A6+%2B+c+ ALIGN=MIDDLE  ALT=\"+-1+=+a%2A6%5E2+%2B+b%2A6+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1+=+36a+%2B+6b+%2B+c+ ALIGN=MIDDLE  ALT=\"+-1+=+36a+%2B+6b+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "You have 3 equation with 3 unknowns, so<BR>\n" );
document.write( "it's solvable<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Plug (2) into (1) and (3)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16a+%2B+4%2A%28+-8a+%29+%2B+c+%2B+3+=+0+ ALIGN=MIDDLE  ALT=\"+16a+%2B+4%2A%28+-8a+%29+%2B+c+%2B+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16a+-+32a+%2B+c+%2B+3+=+0+ ALIGN=MIDDLE  ALT=\"+16a+-+32a+%2B+c+%2B+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16a+%2B+c+%2B+3+=+0+ ALIGN=MIDDLE  ALT=\"+-16a+%2B+c+%2B+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36a+%2B+6%2A%28+-8a+%29+%2B+c+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+36a+%2B+6%2A%28+-8a+%29+%2B+c+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12a+%2B+c+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+-12a+%2B+c+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "Subtract (1) from (3)<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12a+%2B+c+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+-12a+%2B+c+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16a+-+c+-+3+=+0+ ALIGN=MIDDLE  ALT=\"+16a+-+c+-+3+=+0+\"   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=+4a+-+2+=+0+ ALIGN=MIDDLE  ALT=\"+4a+-+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+=+2+ ALIGN=MIDDLE  ALT=\"+4a+=+2+\"   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%2F2+ ALIGN=MIDDLE  ALT=\"+a+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-8a+ ALIGN=MIDDLE  ALT=\"+b+=+-8a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4+ ALIGN=MIDDLE  ALT=\"+b+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12a+%2B+c+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+-12a+%2B+c+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12%2A%28+1%2F2%29+%2B+c+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+-12%2A%28+1%2F2%29+%2B+c+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6+%2B+c+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+-6+%2B+c+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+5+ ALIGN=MIDDLE  ALT=\"+c+=+5+\"   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+=+%281%2F2%29%2Ax%5E2+-+4x+%2B+5+ ALIGN=MIDDLE  ALT=\"+y+=+%281%2F2%29%2Ax%5E2+-+4x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "( 4, -3 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3+=+%281%2F2%29%2A4%5E2+-+4%2A4+%2B+5+ ALIGN=MIDDLE  ALT=\"+-3+=+%281%2F2%29%2A4%5E2+-+4%2A4+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3+=+8+-+16+%2B+5+ ALIGN=MIDDLE  ALT=\"+-3+=+8+-+16+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3+=+-3+ ALIGN=MIDDLE  ALT=\"+-3+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "and<BR>\n" );
document.write( "( 6, -1 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1+=+%281%2F2%29%2A6%5E2+-4%2A6+%2B+5+ ALIGN=MIDDLE  ALT=\"+-1+=+%281%2F2%29%2A6%5E2+-4%2A6+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1+=+18+-+24+%2B+5+ ALIGN=MIDDLE  ALT=\"+-1+=+18+-+24+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1+=+-1+ ALIGN=MIDDLE  ALT=\"+-1+=+-1+\"   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+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29%2Ax%5E2+-+4x+%2B+5+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29%2Ax%5E2+-+4x+%2B+5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looks OK<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );