document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163607>Question 163607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the answers to a, b,c for for the quadratic function y= -x^2 + 6x -5\r<BR>\n" );
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document.write( "a) Find the co-ordinates of the vertex of the parabola<BR>\n" );
document.write( "b) Find the equation of the axis of symmetry<BR>\n" );
document.write( "c) Find the maximum or minimum value\r<BR>\n" );
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document.write( "Here is what I have - I must say my concern is the - (negative) in front of the -x^2.\r<BR>\n" );
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document.write( "a) x = - b/2a = - 6/2(-1) = 3  and y = (-3^2) + 6(3) - 5 = -9 +18 - 5 = 4\r<BR>\n" );
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document.write( "b) ? is this x = 3<BR>\n" );
document.write( "c)   x |  y<BR>\n" );
document.write( "     -------<BR>\n" );
document.write( "     0    -5<BR>\n" );
document.write( "     1     0<BR>\n" );
document.write( "     2     3<BR>\n" );
document.write( "     3     4<BR>\n" );
document.write( "     4     3<BR>\n" );
document.write( "     5     0<BR>\n" );
document.write( "     6     -5\r<BR>\n" );
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document.write( "   Based on this maximum is 4\r<BR>\n" );
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document.write( "Thanks for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120562 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=120562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Congratulations for making an attempt at solving this problem!<BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2%2B6x-5 ALIGN=MIDDLE  ALT=\"y+=+-x%5E2%2B6x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find:<BR>\n" );
document.write( "a) The vertex of the parabola:<BR>\n" );
document.write( "The x-coordinate is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > In your equation, a = -1 and b = 6, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-6%2F2%28-1%29 ALIGN=MIDDLE  ALT=\"x+=+-6%2F2%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > You got this part correct! Now substitute this into the original equation to find the y-coordinate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%283%29%5E2%2B6%283%29-5 ALIGN=MIDDLE  ALT=\"y+=+-%283%29%5E2%2B6%283%29-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-9%2B18-5 ALIGN=MIDDLE  ALT=\"y+=+-9%2B18-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4 ALIGN=MIDDLE  ALT=\"y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > You also got this correct!<BR>\n" );
document.write( "The vertex is located at (3, 4) but please note, in your calculations, you show...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2+=+-9 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this is not correct.<BR>\n" );
document.write( "Remember that: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2+=+%28-3%29%28-3%29 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2+=+%28-3%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > but, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%283%29%5E2+=+-%283%29%283%29 ALIGN=MIDDLE  ALT=\"-%283%29%5E2+=+-%283%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The axis of symmetry is the vertical line that bisects the parabola and, of course, it runs right through the vertex, so its equation would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum or minimum value?<BR>\n" );
document.write( "Well, 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, so this indicates that the parabola opens downward, hence, the vertex will be a maximum, and its location is, as you have already found, (3, 4).<BR>\n" );
document.write( "Let's see what the graph looks like for this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C8%2C-5%2C5%2C-x%5E2%2B6x-5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C8%2C-5%2C5%2C-x%5E2%2B6x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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