Answer:
The function reveals that the maximum earning from ticket sales will be $6480 after 2 ($0.50) price increases
Step-by-step explanation:
* Lets explain how to solve the problem
- The function f(x) = -20x² + 80x + 6400 represents the total
earnings from ticket sales and x represents the number of $0.50
price increases
∵ f(x) is a quadratic function
∵ The coefficient of x² is -20
∴ The function has a maximum value
- The vertex of the quadratic function f(x) = ax² + bx + c is (h , k),
where h = -b/2a and k = f(h)
* Lets find the maximum point of f(x)
∵ a = -20 , b = 80
∵ h = -b/2a
∴ h = -(80)/2(-20) = -80/-40 = 2
∵ k = f(h) and h = 2
∴ f(2) = -20(2)² + 80 (2) + 6400
∴ f(2) = -80 + 160 + 6400
∴ f(2) = 6480
∴ k = 6480
* The function reveals that the maximum earning from ticket sales
will be $6480 after 2 ($0.50) price increases
