document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176899>Question 176899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this one...the directions are to find the vertex, the line of symmetry, the minimum and maximum value of the quadratic equation and then graph it.  I know that once I get the vertex, I can find the rest.  I have solved it close to the end, but I am not sure where to go from here...<BR>\n" );
document.write( "f(x)=-2x^2+2x+7<BR>\n" );
document.write( "I used the equation -b+- the square root of b^2-4ac divided by 2a<BR>\n" );
document.write( "I got to -2+-the square root of 60 divided by 4. Now I am stuck...thank you for the help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132019 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=132019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, line-of-symmetry, minimum or (not and) maximum of:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-2x%5E2%2B2x%2B7 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-2x%5E2%2B2x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First, since your are not asked to find the x-intercepts, you didn't need to use the quadratic formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice that the coefficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is negative (-2), so this means that the parabola opens downward and, cosequently, the parabola will have a maximum, not a minimum.<BR>\n" );
document.write( "Note, a parabola cannot have both a maximum and a minimum.<BR>\n" );
document.write( "The maximum point will occur at the vertex of the parabola, so let's find the location of the vertex.<BR>\n" );
document.write( "The x-coordinate of the vertex is given by:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and, in this equation, a = -2, b = 2, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2%29%2F2%28-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2%29%2F2%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F2 ALIGN=MIDDLE  ALT=\"x+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.5 ALIGN=MIDDLE  ALT=\"x+=+0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now to find the y-coordinate, substitute this into the given equation, after replacing f(x) with y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2%281%2F2%29%5E2%2B2%281%2F2%29%2B7 ALIGN=MIDDLE  ALT=\"y+=+-2%281%2F2%29%5E2%2B2%281%2F2%29%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2%281%2F4%29%2B2%281%2F2%29%2B7 ALIGN=MIDDLE  ALT=\"y+=+-2%281%2F4%29%2B2%281%2F2%29%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1%2F2+%2B+1+%2B+7 ALIGN=MIDDLE  ALT=\"y+=+-1%2F2+%2B+1+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+7.5 ALIGN=MIDDLE  ALT=\"y+=+7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex location is (0.5, 7.5) and this is also the location of the maximum point of the parabola.<BR>\n" );
document.write( "The equation of the line of symmetry is simply the equation of the vertical line that passes through the vertex, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.5 ALIGN=MIDDLE  ALT=\"x+=+0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let's look at the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C10%2C-2x%5E2%2B2x%2B7%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C10%2C-2x%5E2%2B2x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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