document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=532173>Question 532173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A) find the coordinates of the vertex and the intercepts<BR>\n" );
document.write( "B) Sketch the graph by hand with at least FIVE points \r<BR>\n" );
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document.write( "y=8-x-2x^2\r<BR>\n" );
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document.write( "I know to rewrite it to y=-2x^2-x=8<BR>\n" );
document.write( "and I found the vertex to be -x/2(-2) which is -1/4 and the graph opens downwards? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350699 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=350699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = -2x^2 -x + 8<BR>\n" );
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document.write( "To find the zeroes, factor or use the quadratic equation:<BR>\n" );
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document.write( "-2x^2 -x + 8 = 0<BR>\n" );
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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-1x%2B8+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-1x%2B8+=+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=%28-1%29%5E2-4%2A-2%2A8=65 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1%29%5E2-4%2A-2%2A8=65\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=65 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--1%2B-sqrt%28+65+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1%2B-sqrt%28+65+%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-%28-1%29%2Bsqrt%28+65+%29%29%2F2%5C-2+=+-2.26556443707464 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+65+%29%29%2F2%5C-2+=+-2.26556443707464\"   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-%28-1%29-sqrt%28+65+%29%29%2F2%5C-2+=+1.76556443707464 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-1%29-sqrt%28+65+%29%29%2F2%5C-2+=+1.76556443707464\"   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-1x%2B8 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-1x%2B8\"   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-1x%2B8+=+-2%28x--2.26556443707464%29%2A%28x-1.76556443707464%29 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-1x%2B8+=+-2%28x--2.26556443707464%29%2A%28x-1.76556443707464%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2.26556443707464, 1.76556443707464.\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-1%2Ax%2B8+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B-1%2Ax%2B8+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "To find the vertex...<BR>\n" );
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document.write( "First, find the axis is symmetry = -b/2a = -(-1)/(2*(-2)) = -1/4<BR>\n" );
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document.write( "Then substitute that value for 'x' and solve for y<BR>\n" );
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document.write( "y = -2(-1/4)^2 -(-1/4) + 8<BR>\n" );
document.write( "y = -2(1/16) +1/4 + 8<BR>\n" );
document.write( "y = -2/16 + 1/4 + 8<BR>\n" );
document.write( "y = -1/8 + 1/4 + 8<BR>\n" );
document.write( "y = 1/8 + 8<BR>\n" );
document.write( "y = 65/8<BR>\n" );
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document.write( "vertex = (-1/4, 65/8)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2%2Ax%5E2-x%2B8%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2%2Ax%5E2-x%2B8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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