document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116065>Question 1116065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A movie theater is considering lowering ticket prices. If it lowers ticket prices by x dollars,<BR>\n" );
document.write( "the expected revenue function per week is r(x)=-500(x-2.5)^+28,025. What decrease in<BR>\n" );
document.write( "ticket prices will produce the maximum revenue for the theater? What is the maximum<BR>\n" );
document.write( "revenue that is possible?\r<BR>\n" );
document.write( "\n" );
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 #731052 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=731052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The revenue function is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29=-500%28x-2.5%29%5E2%2B%2228%2C025%22 ALIGN=MIDDLE  ALT=\"r%28x%29=-500%28x-2.5%29%5E2%2B%2228%2C025%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "When you do not remember \"formulas\"<BR>\n" );
document.write( "and other calculation tricks and problem-solving recipes taught in class,<BR>\n" );
document.write( "using your own brain may work, if a little slower.<BR>\n" );
document.write( " <BR>\n" );
document.write( "You do not need to have been awake during the classes about quadratic functions to know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2.5%29%5E2%3E=0 ALIGN=MIDDLE  ALT=\"%28x-2.5%29%5E2%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > no matter what real number value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2.5%29 ALIGN=MIDDLE  ALT=\"%28x-2.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > take;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-500%28x-2.5%29%5E2%3C=0 ALIGN=MIDDLE  ALT=\"-500%28x-2.5%29%5E2%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > no matter what, and as a consequence<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29=-500%28x-2.5%29%5E2%2B%2228%2C025%22%3C=0%2B%2228%2C025%22=%2228%2C025%22 ALIGN=MIDDLE  ALT=\"r%28x%29=-500%28x-2.5%29%5E2%2B%2228%2C025%22%3C=0%2B%2228%2C025%22=%2228%2C025%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > no matter what.<BR>\n" );
document.write( " <BR>\n" );
document.write( "You should also realize that the only way to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29=%2228%2C025%22 ALIGN=MIDDLE  ALT=\"r%28x%29=%2228%2C025%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-500%28x-2.5%29%5E2=0 ALIGN=MIDDLE  ALT=\"-500%28x-2.5%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2.5%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-2.5%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2.5=0 ALIGN=MIDDLE  ALT=\"x-2.5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=2.5%29 ALIGN=MIDDLE  ALT=\"highlight%28x=2.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "So, if (and only if)<BR>\n" );
document.write( "the movie theater lowers ticket prices by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282.5%29 ALIGN=MIDDLE  ALT=\"highlight%282.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars,<BR>\n" );
document.write( "they can expect the maximum predicted revenue of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2428%2C025%22 ALIGN=MIDDLE  ALT=\"%22%2428%2C025%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE: Quadratic functions graph as parabolas,<BR>\n" );
document.write( "with a maximum (if the coefficient of the squared term is negative),<BR>\n" );
document.write( "or a minimum (if that coefficient is positive).<BR>\n" );
document.write( "They can be found in the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2=k ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2=k\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "Where a,b,c,h, and k are constants,<BR>\n" );
document.write( "but it must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E0 ALIGN=MIDDLE  ALT=\"a%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or it is not a quadratic function).<BR>\n" );
document.write( "You can also find them in any other equivalent form that your teacher could choose.<BR>\n" );
document.write( "It will be up to you to recognize what you are dealing with.<BR>\n" );
document.write( "If your teacher is merciful, the function will look like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2=k ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2=k\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and as explained at the top <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=h ALIGN=MIDDLE  ALT=\"x=h\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be<BR>\n" );
document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > value where the maximum or minimum happens,<BR>\n" );
document.write( "and that maximum or minimum value of the function will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If the quadratic function appears in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you could transform it to the equivalent, but more useful form,<BR>\n" );
document.write( "or you could remember that the maximum or minimum happens for'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F%222+a%22 ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F%222+a%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );