document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=730485>Question 730485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help in writing a word problem involving a quadratic function. And I need to explain it in terms someone not in class could understand it, please. I am in the home stretch of my class and would really appreciate the help. Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446691 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=446691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "A function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a quadratic function if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > are real numbers and not equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "The graph of a quadratic function is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parabola ALIGN=MIDDLE  ALT=\"parabola\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The most basic aid in graphing a parabola is knowing whether <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3E+0 ALIGN=MIDDLE  ALT=\"a+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the graph opens <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=upward ALIGN=MIDDLE  ALT=\"upward\"   DISABLED_style= \"max-width:90%; height:auto;\" >) or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+0 ALIGN=MIDDLE  ALT=\"a+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the graph opens <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=downward ALIGN=MIDDLE  ALT=\"downward\"   DISABLED_style= \"max-width:90%; height:auto;\" >). \r<BR>\n" );
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document.write( "The two simplest quadratic functions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+-+x%5E2 ALIGN=MIDDLE  ALT=\"g%28x%29+=+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( " a word problem involving a quadratic function:\r<BR>\n" );
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document.write( "An inquiry shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60000 ALIGN=MIDDLE  ALT=\"60000\"   DISABLED_style= \"max-width:90%; height:auto;\" > students will attend a theater play in one week if the ticket price is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars. Suppose that for every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.50 ALIGN=MIDDLE  ALT=\"2.50\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars added to the ticket price, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000 ALIGN=MIDDLE  ALT=\"2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > fewer students will attend the play.\r<BR>\n" );
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document.write( "1. What ticket price will give the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=greatest ALIGN=MIDDLE  ALT=\"greatest\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=revenue ALIGN=MIDDLE  ALT=\"revenue\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the week?<BR>\n" );
document.write( "2. what is the approximate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=maximum ALIGN=MIDDLE  ALT=\"maximum\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=possible ALIGN=MIDDLE  ALT=\"possible\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=profit ALIGN=MIDDLE  ALT=\"profit\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the week if the theater play spends approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > million dollars to have the play showed for one week?\r<BR>\n" );
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document.write( "answer:\r<BR>\n" );
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document.write( "1. Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the number of times $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.50 ALIGN=MIDDLE  ALT=\"2.50\"   DISABLED_style= \"max-width:90%; height:auto;\" > is added to the ticket price (and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000 ALIGN=MIDDLE  ALT=\"2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > fewer students attend).\r<BR>\n" );
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document.write( "Revenue for the week is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840%2B2.50x%29%2860000-2000x%29 ALIGN=MIDDLE  ALT=\"%2840%2B2.50x%29%2860000-2000x%29\"   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=2.5%2816%2Bx%29%2A2000%2830-x%29 ALIGN=MIDDLE  ALT=\"2.5%2816%2Bx%29%2A2000%2830-x%29\"   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=5000%2816%2Bx%29%2830-x%29 ALIGN=MIDDLE  ALT=\"5000%2816%2Bx%29%2830-x%29\"   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=5000%28-x%5E2%2B14x%2B480%29 ALIGN=MIDDLE  ALT=\"5000%28-x%5E2%2B14x%2B480%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thus the greatest revenue is given by the maximum of function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B14x%2B480 ALIGN=MIDDLE  ALT=\"-x%5E2%2B14x%2B480\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It is a quadratic function with a maximum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a=+-14%2F%28-2%29=7 ALIGN=MIDDLE  ALT=\"-b%2F2a=+-14%2F%28-2%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which the revenue will be greatest. <BR>\n" );
document.write( "To answer the question, calculate the corresponding ticket price by adding $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.50%2A7 ALIGN=MIDDLE  ALT=\"2.50%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the original $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40=40%2B2.5%2A7=57.50 ALIGN=MIDDLE  ALT=\"40=40%2B2.5%2A7=57.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Profit=revenue+-+spending ALIGN=MIDDLE  ALT=\"Profit=revenue+-+spending\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since spendings are fixed, maximum profit is obtained when maximum revenue is obtained as above, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Max+_profit=5000%28-7%5E2%2B14%2A7%2B480%29-1500000 ALIGN=MIDDLE  ALT=\"Max+_profit=5000%28-7%5E2%2B14%2A7%2B480%29-1500000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1145000 ALIGN=MIDDLE  ALT=\"1145000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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