Question

Tico’s Taco Truck is trying to determine the best price at which to sell tacos, the only item on the menu, to maximize profits. The taco truck’s owner decides to adjust the price per taco and record data on the number of tacos sold each day with each new price. When the taco truck charges $4 for a taco, it sells an average of 60 tacos in one day. With every $1 increase in the price of a taco, the number of tacos sold per day decreases by 7. The owner can calculate the daily revenue using the polynomial expression -7x2 + 32x + 240, where x is the number of $1 increases in the taco price. In this activity, you’ll interpret and manipulate this expression and the scenario it represents. Part D: What are some advantages of writing the polynomial expression -7x2 + 32x + 240 in factored form when interpreting this situation?

Answer 1

The constant term is 240. It represents the initial daily revenue.

Explanation:

It is given that Tico's Taco Truck is trying to determine the best price at which to sell tacos, the only item on the menu, to maximize profits.

The owner can calculate the daily revenue using the polynomial expression

where x is the number of $1 increases in the taco price.

Constant term does not contain any variable.

In the given expression 240 is free from variable x. So, the constant term is 240.

The value of expression is 240 for x=0. Since x is the number of $1 increases in the taco price, therefore 240 is the daily revenue when the taco price is not increased or the taco price increased by 0.

Therefore the constant term is 240 and it represents the initial daily revenue.