A company that sells movies online is deciding how much to charge customers to download a new movie. Based on data from previous sales, the company predicts that if they charge dollars for each download, then the number of downloads, in thousands, is .

1. Complete the table to show the predicted number of downloads at each listed price. Then find the revenue at each price. The first row has been completed for you.

   price (dollars per download)	number of downloads (thousands)	revenue (thousands of dollars)
   3	15	45
   5
   10
   12
   15
   18

2. Is the relationship between the price of the movie and the revenue (in thousands of dollars) quadratic? Explain how you know.

3. Plot the points that represent the revenue, , as a function of the price of one download in dollars, .

   

   Blank coordinate plane with grid, origin O. Horizontal axis scale 0 to 25 by 5’s, labeled “price (dollars per download)”. Vertical axis scale 0 to 200 by  50’s, labeled “revenue (thousands of dollars)”.

4. What price would you recommend that the company charge for a new movie? Explain your reasoning.

Here are four sets of descriptions and equations that represent some familiar quadratic functions. The graphs show what graphing technology may produce when the equations are graphed. For each function:

• Describe a domain that is appropriate for the situation. Think about any upper or lower limits for the input, as well as whether all numbers make sense as the input. Then, describe how the graph should be modified to show the domain that makes sense.
• Identify or estimate the vertex on the graph. Describe what it means in the situation.
• Identify or estimate the zeros of the function. Describe what they meant in the situation.

1. The area of a rectangle with a perimeter of 25 meters and a side length of :

   

   Graph of the quadratic function on a coordinate plane, origin . Horizontal axis scale negative 10 to 15 by 5s, labeled “length (meters)”. Vertical axis scale 0 to 60 by 10’s, labeled “area (square meters)”. Some of the points of this function are (0 comma 0), (1 comma 11 point 5) and (5 comma 37 point 5) to a maximum at (6 point 2 5 comma 39 point 0 6 3) then decreasing through (10 comma 25), (12 comma 6) and (12 point 5 comma 0).

   • Domain:

   • Vertex:

   • Zeros:

2. The number of squares as a function of step number :

   

   Graph of the quadratic function on a coordinate plane, origin . Horizontal axis scale negative 12 to 12 by 6’s, labeled “step number”. Vertical axis scale 0 to 200 by 40’s, labeled “number of squares”. Some of the points of this function are (negative 10 comma 104), (negative 6 comma 40) and (negative 3 comma 13) to a minimum at (0 comma 4) then increasing through (3 comma 13), (6 comma 40) and (10 comma 104).

   • Domain:

   • Vertex:

   • Zeros:​​​

3. The distance, in feet, that an object has fallen seconds after being dropped:

   

   Graph of the quadratic function  on a coordinate plane, origin . Horizontal axis scale negative 8 to 8 by 4’s, labeled “time (seconds)”. Vertical axis scale 0 to 600 by 200’s, labeled “distance fallen (feet)”. Some of the points of this function are (negative 8 comma 1024), (negative 5 comma 400) and (negative 1 comma 16) to a minimum at (0 comma 0) then increasing through (1 comma 16), (5 comma 400) and (8 comma 1024).

   • Domain:

   • Vertex:

   • Zeros:

4. The height, in feet, of an object seconds after being dropped:

   

   Graph of the quadratic function h(t)=576 - 16t^2 on a coordinate plane, origin O. Horizontal axis scale negative 8 to 8 by 4’s, labeled “time (seconds)”. Vertical axis scale 0 to 800 by 200’s, labeled “height (feet)”. Some of the points of this function are (negative 6 comma 0), (negative 4 comma 320) and (negative 2 comma 512) to a maximum at (0 comma 576) then decreasing through (2 comma 512), (4 comma 320) and (6 comma 0).

   • Domain:

   • Vertex:

   • Zeros: