Quadratic Word Problems

A local sports team models its ticket sales revenue, in thousands of dollars, with the function

f(x) = 5x² +15x -90

where x represents the number of games played. How many games must the team play for its revenue to be $0?

A movie theater models its weekly profit, in thousands of dollars, with the function

m(x) = 5x² – 5x – 210,

where x is the number of movie screenings per day. How many screenings must be held for the theater to break even?

A car rental company models its daily earnings, in thousands of dollars, using the function

c(x) = 4x² – 20x – 200,

where x is the number of cars rented. How many cars must be rented for the company to break even?

A tech startup models its monthly expenses, in thousands of dollars, using the function
t(x) = 4x² + 16x – 240,

where x represents the number of software licenses sold. How many software licenses must be sold for the company to break even?

A fitness center models its monthly profit, in thousands of dollars, with the function

f(x) = 2x² – 4x – 96,

where x represents the number of new memberships sold. How many memberships must be sold for the center to break even?

A gadget manufacturer models its profit, in thousands of dollars, with the function

m(x) = 2x² – 2x – 40,

where x is the number of gadgets sold. How many gadgets must the company sell to have a net income of $0?

• A restaurant uses the function

• r(x) = 6x² – 12x – 144

• to model its daily revenue in thousands of dollars, where x represents the number of customers served. How many customers must the restaurant serve for its revenue to reach zero?

The student council organizes a dance and models its profit, in dollars, with the function

f(x) = 4x² – 12x – 160,

where x is the number of tickets sold. How many tickets must be sold for the council to make no profit or loss?

A math club models its competition fees, in dollars, with the function

f(x) = 5x² – 30x – 135,

where x is the number of students participating. How many students must sign up for the competition for the club to break even?

The football team is selling Discount Cards at games to raise money. Their earnings, in dollars, follow the function

f(x) = 6x² – 36x – 42,

where x is the number of snack packs sold. How many Discount Cards must they sell to avoid a loss?