Question 96325
The word problem reads as follows: An event coordinator for a theater has requested information about projected ticket sales. you provide him 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). Tickets = -0.2x^2+12x+11.
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A. does the graph of the equation open up or down and how this is determined?
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It opens downward. This can be determined by the fact that the coefficient of the squared term  (-2x^2 in this equation) in a quadratic equation, is negative. It also means that it has a maximum. 
If it were positive, it would  open up-ward and have a minimum
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b. What happens to ticket sales as time passes?
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Drawing the actual graph of this equation will make it easy to understand:
{{{ graph( 300, 200, -10, 80, -20, 200, -.2x^2+12x+11) }}}
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Since it has a maximum, You can see ticket sales increase to a maximum
at about day 30 then decrease to 0 on about day 60
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c. use the equation to determine the last day that tickets will be sold.
You can determine this without the graph by make the equation = 0 and solving
for x:
-.2x^2 + 12x + 11 = 0
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The quadratic formula is needed here: a= -.2; b = 12; c = 11
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
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{{{x = (-12 +- sqrt( 12^2 - 4 * -.2 * 11 ))/(2*-.2) }}}
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{{{x = (-12 +- sqrt( 144 - (-8.8) ))/(-.4) }}}
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{{{x = (-12 +- sqrt( 144 + 8.8 ))/(-.4) }}}
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{{{x = (-12 +- sqrt( 152.8))/(-.4) }}}
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{{{x = (-12 - 12.36)/-.4}}}; we only want the positive solution here
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{{{x = (-24.36)/-.4}}}
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x = +60.9 or on the 61st day, no tickets sold, so day 60 would be the last day 
that tickets are sold, note that is what the graph indicates.
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In fact if you substitute 60 for x in the graph, you will see that 11 tickets
were sold on the last day
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You can plot this graph yourself using this table
 x | y
-------
-1 |neg
 0 | 11
10 |111
20 |171
30 |191
40 |171
50 |111
60 | 11
70 | neg
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That should help you see what's going on here, Any question?