Concept explainers
a.
To write: The verbal model and a quadratic function that represents the weekly profit of the theater.
Verbal model:
Quadratic model:
Given information:
The theater sells 150 tickets to a play weekly when the price is $20, and for each $1 decrease in the price, the sale increases by 10 tickets per week.
Concept used:
Profit = Revenue − cost
Calculation:
Since the profit revenue minus total cost, the verbal model for the theater’s profit can be given as:
Let the price be decreased
So, the price of the ticket becomes
Then, the revenue will be
Therefore, the function modelling the situation can be written as follows:
b.
To make: A table of values for the quadratic function.
Given information:
The theater sells 150 tickets to a play weekly when the price is $20, and for each $1 decrease in the price, the sale increases by 10 tickets per week.
Concept used:
Take a random value of x and substitute in the function to find the value of y, and then use the pair of points to make the table.
Calculation:
The quadratic function for the situation is
When
When
When
When
Now, construct the table based on these values.
c.
To graph and find: The graph of the quadratic function using the table and then find how the theater can maximize the profit.
The theater can maximize the profit offering each ticket for
Given information:
The theater sells 150 tickets to a play weekly when the price is $20, and for each $1 decrease in the price, the sale increases by 10 tickets per week.
Concept used:
The vertex of the quadratic function represents the maximum/minimum point of the function.
Calculation:
Plot the points found in part (b) and join them with a smooth curve as follows:
Observe that the vertex of the quadratic function is at the point
When
Therefore, the theater can maximize the profit offering each ticket for
Conclusion:
The theater can maximize the profit offering each ticket for
Chapter 1 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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