document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204250>Question 204250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you complete this function equation f(x)=-2x^2+8x-5. I need to find the vertex h,k , compute h and k and graph the quadratic equation. Plus find the max value of f where it occurs. \r<BR>\n" );
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document.write( "I started the equation and found h. \r<BR>\n" );
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document.write( "a=-2 b=8 c=-5, so using the ormula -b/2a I got -8/2(-2) which gave me -8/-4 which gave me 2. h=2. Where do I go from here? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154213 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154213\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do you complete this function equation f(x)=-2x^2+8x-5. I need to find the vertex h,k , compute h and k and graph the quadratic equation. Plus find the max value of f where it occurs.<BR>\n" );
document.write( "I started the equation and found h.<BR>\n" );
document.write( "a=-2 b=8 c=-5, so using the ormula -b/2a I got -8/2(-2) which gave me -8/-4 which gave me 2. h=2. Where do I go from here?<BR>\n" );
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document.write( "What you found:<BR>\n" );
document.write( "-b/2a = 2 <BR>\n" );
document.write( "is the \"axis of symmetry\"<BR>\n" );
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document.write( "To find 'k', simply plug 2 back into the equation and solve:<BR>\n" );
document.write( "f(x)=-2x^2+8x-5<BR>\n" );
document.write( "f(2)=-2(2)^2+8(2)-5<BR>\n" );
document.write( "f(x)=-8+16-5<BR>\n" );
document.write( "f(x)=3<BR>\n" );
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document.write( "So, (h,k) = (2,3) vertex<BR>\n" );
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document.write( "To plot, looking at the 'a' coefficient (-2), we KNOW it is a parabola that opens downward.  Use the \"vertex\" above and find two additional points to plot.  The two additional points could be where the parabola crosses the x-axis:<BR>\n" );
document.write( "0=-2x^2+8x-5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<TABLE  BORDER=1>\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%2B8x%2B-5+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B8x%2B-5+=+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=%288%29%5E2-4%2A-2%2A-5=24 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%288%29%5E2-4%2A-2%2A-5=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=24 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+=+%28-8%2B-sqrt%28+24+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-8%2B-sqrt%28+24+%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-%288%29%2Bsqrt%28+24+%29%29%2F2%5C-2+=+0.775255128608411 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%288%29%2Bsqrt%28+24+%29%29%2F2%5C-2+=+0.775255128608411\"   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-%288%29-sqrt%28+24+%29%29%2F2%5C-2+=+3.22474487139159 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%288%29-sqrt%28+24+%29%29%2F2%5C-2+=+3.22474487139159\"   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%2B8x%2B-5 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B8x%2B-5\"   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%2B8x%2B-5+=+-2%28x-0.775255128608411%29%2A%28x-3.22474487139159%29 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B8x%2B-5+=+-2%28x-0.775255128608411%29%2A%28x-3.22474487139159%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.775255128608411, 3.22474487139159.\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%2B8%2Ax%2B-5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B8%2Ax%2B-5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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