1. Module 7.12
Next Year’s Gig

2. the number of people who will buy a ticket after x number of $1 price increases
the ticket price after x number
of $1 price increases

3. –20x2 + 7400x + 240000 8000*$30 = $240,000 (the c value!)
(−30, 0) and (400, 0).  The x-intercepts represent the number of $1 increases in ticket prices that would result in $0 in income.
***Reminder: The axis of symmetry can be found as the midpoint of the x-intercepts!!

4. Try #2 with your table

5. the number of people who will buy a ticket after x number of $1 price increases
the ticket price after x number
of $1 price increases
−18x x
$320,000

6. This is the y-intercept
8000*$40 = $320,000 is the c value
This is the y-intercept
The vertex is at (202.2, ). This means there are 202 $1 increases to the original ticket price. The new price would be $242 since the original price was $40. The maximum income is $1,056,088.88

7. −38x x

8. The y-intercept of B(x) is the sum of the y-intercepts of J(x) and A(x).  Since we are adding the functions together, we add the y-values corresponding to the same x-values.
The maximum of B(x) is larger than the maximums of J(x) and A(x) but that is due to the context of adding incomes together.  The maximum of the combined function is not generally the sum of the maximums of the original functions. This is because when you add two functions together, you are adding y-values for corresponding x-values. The vertices do not have the same x-values.