document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936233>Question 936233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> transform the quadratic function y=-2x^2-12x-10 into vertex form. find the vertex, x and y intercepts. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569671 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><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=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569671\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> step 1 : determination of vertex<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+-2x%5E2-12x-10 ALIGN=MIDDLE  ALT=\"+y=+-2x%5E2-12x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+-2%28x%5E2%2B6x%2B5%29 ALIGN=MIDDLE  ALT=\"+y=+-2%28x%5E2%2B6x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+-2%28x%5E2%2B2%2Ax%2A3%2B3%5E2-4%29 ALIGN=MIDDLE  ALT=\"+y=+-2%28x%5E2%2B2%2Ax%2A3%2B3%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+-2%28%28x%2B3%29%5E2-4%29 ALIGN=MIDDLE  ALT=\"+y=+-2%28%28x%2B3%29%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+-2%28x%2B3%29%5E2-2%28-4%29 ALIGN=MIDDLE  ALT=\"+y=+-2%28x%2B3%29%5E2-2%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+-2%28x%2B3%29%5E2%2B8+ ALIGN=MIDDLE  ALT=\"+y=+-2%28x%2B3%29%5E2%2B8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  vertex form   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"++y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  vertex   =(h,k)<BR>\n" );
document.write( "  hence vertex  (h,k) =(-3,8)<BR>\n" );
document.write( "step 2<BR>\n" );
document.write( "determination of y-intercept:<BR>\n" );
document.write( " keep x=o in the  y= -2x^2-12x-10<BR>\n" );
document.write( "                 y= -2*0-12*0 -10<BR>\n" );
document.write( "           y= -10 <BR>\n" );
document.write( " hence y-intercept  = -10\r<BR>\n" );
document.write( "\n" );
document.write( "step 3<BR>\n" );
document.write( "Determination of x-intercept:<BR>\n" );
document.write( "keep y= 0 in  y= -2x^2-12x-10<BR>\n" );
document.write( "          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0=+-2x%5E2-12x-10 ALIGN=MIDDLE  ALT=\"+0=+-2x%5E2-12x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         <TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B-12x%2B-10+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-12x%2B-10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-12%29%5E2-4%2A-2%2A-10=64 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-12%29%5E2-4%2A-2%2A-10=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=64 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--12%2B-sqrt%28+64+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--12%2B-sqrt%28+64+%29%29%2F2%5Ca\"   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=x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+64+%29%29%2F2%5C-2+=+-5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+64+%29%29%2F2%5C-2+=+-5\"   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+=+%28-%28-12%29-sqrt%28+64+%29%29%2F2%5C-2+=+-1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-12%29-sqrt%28+64+%29%29%2F2%5C-2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B-12x%2B-10 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-12x%2B-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B-12x%2B-10+=+-2%28x--5%29%2A%28x--1%29 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-12x%2B-10+=+-2%28x--5%29%2A%28x--1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -5, -1.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B-12%2Ax%2B-10+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B-12%2Ax%2B-10+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "             <BR>\n" );
document.write( "hence x-intercepts are -5,  -1 \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );