document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141054>Question 141054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. (x=1  is the day tickets go on sale).   <BR>\n" );
document.write( "Tickets = -0.2x^2+12x+11			  \r<BR>\n" );
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document.write( "	a. Does the graph of this equation open up or down? How did you determine this? <BR>\n" );
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document.write( "b. Describe what happens to the tickets sales as time passes? \r<BR>\n" );
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document.write( "c. Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)<BR>\n" );
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document.write( "d. Will tickets peak or be at a low during the middle of the sale? How do you know? <BR>\n" );
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document.write( "e. After how many days will the peak or low occur? <BR>\n" );
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document.write( "f. How many tickets will be sold on the day when the peak or low occurs? <BR>\n" );
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document.write( "g. What is the point of the vertex? How does this number relate to your answers in parts e and f? <BR>\n" );
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document.write( "h. How many solutions are there to the equation ? How do you know? <BR>\n" );
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document.write( "i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102856 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=102856\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. (x=1 is the day tickets go on sale).<BR>\n" );
document.write( "Tickets = -0.2x^2+12x+11<BR>\n" );
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document.write( "The best way to do this, is to make the actual graph of the equation<BR>\n" );
document.write( "it should look like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+75%2C+-20%2C+200%2C+-0.2x%5E2%2B12x%2B11%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+75%2C+-20%2C+200%2C+-0.2x%5E2%2B12x%2B11%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "a. Does the graph of this equation open up or down? How did you determine this?<BR>\n" );
document.write( "Look at it<BR>\n" );
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document.write( "b. Describe what happens to the tickets sales as time passes?<BR>\n" );
document.write( "You could say the sales increase, reach a peak, then decrease to 0<BR>\n" );
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document.write( "c. Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)<BR>\n" );
document.write( "Solve -0.2x^2+12x+11 = 0 using the quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The positive solution will be about approx x = 61.  (60th day of ticket sales)<BR>\n" );
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document.write( "d. Will tickets peak or be at a low during the middle of the sale? How do you know? <BR>\n" );
document.write( "Look at the graph<BR>\n" );
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document.write( "e. After how many days will the peak or low occur?<BR>\n" );
document.write( "Look at the graph<BR>\n" );
document.write( "Find the axis of symmetry: x = -b/(2a); a=-.2; b=12<BR>\n" );
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document.write( "f. How many tickets will be sold on the day when the peak or low occurs?<BR>\n" );
document.write( "Find the vertex using the above x value<BR>\n" );
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document.write( "g. What is the point of the vertex? How does this number relate to your answers in parts e and f?<BR>\n" );
document.write( "That is the max<BR>\n" );
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document.write( "h. How many solutions are there to the equation ? How do you know?<BR>\n" );
document.write( "This equation has two solution, but only the positive solution makes sense<BR>\n" );
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document.write( "i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? </SPAN>\n" );
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