Revenue and Quadratic Functions

The video tutorial explains how to determine the ticket price that maximizes revenue for a stadium with a seating capacity of 1000. Initially, with a ticket price of $30, the attendance is 400 people. For each $1 decrease in price, attendance increases by 50. The tutorial guides viewers through setting up a revenue equation as a function of price decreases, solving it using the vertex formula to find the maximum revenue point, and determining the optimal ticket price of $19. The video concludes with an invitation to explore similar quadratic word problems.

What type of mathematical problem is being discussed in the video?

• Logarithmic equation

• Exponential equation

• Quadratic equation

• Linear equation

What is the seating capacity of the stadium mentioned in the video?

• 1500

• 1000

• 2000

• 500

What is the initial ticket price before any decreases?

• $30

• $35

• $25

• $20

What is the initial attendance when the ticket price is $30?

• 300 people

• 350 people

• 400 people

• 450 people

How does attendance change with each $1 decrease in ticket price?

• Increases by 30

• Increases by 50

• Increases by 60

• Increases by 40

What is the formula for revenue in terms of ticket price and attendance?

• Revenue = Price + Attendance

• Revenue = Price - Attendance

• Revenue = Price x Attendance

• Revenue = Price / Attendance

What happens to the attendance if the ticket price is decreased by $2?

• Increases by 50

• Increases by 100

• Increases by 200

• Increases by 150

What is the initial revenue equation before expansion?

• R = (30 - X)(400 + 50X)

• R = (30 + X)(400 - 50X)

• R = (30 + X)(400 + 50X)

• R = (30 - X)(400 - 50X)

What is the revenue when there are no price decreases?

• $12,000

• $16,000

• $10,000

• $14,000

What is the expanded form of the revenue equation?

• R = 50X^2 - 1100X + 12000

• R = -50X^2 + 1100X + 12000

• R = -50X^2 - 1100X + 12000

• R = 50X^2 + 1100X + 12000