document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149596>Question 149596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the maximum value of the function f(x) = (3-x)(5x + 35)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109736 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=109736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, we need to find the zeros. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-x%29%285x+%2B+35%29=0 ALIGN=MIDDLE  ALT=\"%283-x%29%285x+%2B+35%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the expression equal to zero.\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-x=0 ALIGN=MIDDLE  ALT=\"3-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+35=0 ALIGN=MIDDLE  ALT=\"5x+%2B+35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now solve for x for each factor:\r<BR>\n" );
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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;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the zeros of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-x%29%285x+%2B+35%29 ALIGN=MIDDLE  ALT=\"%283-x%29%285x+%2B+35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <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;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now average the zeros to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B%28-7%29%29%2F2=%28-4%29%2F%282%29=-2 ALIGN=MIDDLE  ALT=\"%283%2B%28-7%29%29%2F2=%28-4%29%2F%282%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the axis of symmetry (ie the x-coordinate of the vertex) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the y coordinate of the vertex \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%283-x%29%285x+%2B+35%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%283-x%29%285x+%2B+35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=%283-%28-2%29%29%285%28-2%29+%2B+35%29 ALIGN=MIDDLE  ALT=\"f%28-2%29=%283-%28-2%29%29%285%28-2%29+%2B+35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=%283%2B2%29%285%28-2%29+%2B+35%29 ALIGN=MIDDLE  ALT=\"f%28-2%29=%283%2B2%29%285%28-2%29+%2B+35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-%28-2%29 ALIGN=MIDDLE  ALT=\"3-%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B2 ALIGN=MIDDLE  ALT=\"3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=%283%2B2%29%28-10+%2B+35%29 ALIGN=MIDDLE  ALT=\"f%28-2%29=%283%2B2%29%28-10+%2B+35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=%285%29%2825%29 ALIGN=MIDDLE  ALT=\"f%28-2%29=%285%29%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=125 ALIGN=MIDDLE  ALT=\"f%28-2%29=125\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So the y coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=125 ALIGN=MIDDLE  ALT=\"y=125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the vertex is at the point (-2,125). Since the vertex is either the highest or lowest point (in this case the highest), this means that that the maximum value of the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125 ALIGN=MIDDLE  ALT=\"125\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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