Question 388399
<font face="Garamond" size="+2">


It opens down because the lead coefficient is negative.


Ticket sales start small, get larger, then get smaller


Set the quadratic equal to zero.  Use the quadratic formula to solve it.  The  integer part of the largest root is the last day of ticket sales.


Divide the opposite of the coefficient on the first degree term by 2 times the lead coefficient to get the value of x where the peak occurs.


Evaluate the function at the value of x determined above to find the number of tickets sold at the peak.


The x-coordinate of the vertex is the day when the peak occurs.  The y-coordinate of the vertex is the number of tickets sold that day.


There are two solutions to the equation.  I know because the value of the function at the vertex is positive and the parabola opens downward, therefore the graph must cross the x-axis in two places.  I also know that there are two solutions because the lead coefficient and the constant coefficient have opposite signs and the quadratic is not a perfect square.


The solutions represent the days when there will be zero ticket sales.  The negative root makes no sense because you can't be selling tickets before you start selling tickets.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>