Understanding Demand Functions

The video tutorial explains a demand function D(Q) = -Q^2 - 2Q + 517, where Q is in thousands of units sold and D(Q) is the price per unit. It covers three main problems: calculating the price for 7,000 units sold, determining the number of units sold at a price of $374, and finding the value of Q where D(Q) crosses the Q-axis. The tutorial uses algebraic manipulation and the quadratic formula to solve these problems, emphasizing the importance of understanding the units and the mathematical process involved.

What does the variable Q represent in the demand function?

• The price per unit in dollars

• The total revenue

• The cost of production

• The number of units sold in thousands

If 7,000 units are to be sold, what is the value of Q used in the demand function?

• 7,000

• 0.007

• 70

• 7

What is the price per unit if 7,000 units are sold?

• $143

• $517

• $374

• $454

When the price is set at $374, what equation do we solve to find Q?

• D(Q) = 374

• Q = 374

• D(Q) = -Q^2 + 2Q - 517

• 374 = -Q^2 - 2Q + 517

How many units can be expected to sell if the price is $374?

• 7,000 units

• 11,000 units

• 21,760 units

• 13,000 units

What method is used to find where the demand function crosses the Q-axis?

• Linear approximation

• Quadratic formula

• Graphical method

• Trial and error

What is the significance of the demand function crossing the Q-axis?

• It marks the minimum cost

• It shows the break-even point

• It indicates the maximum price

• It represents the quantity demanded when the price is zero

What is the approximate value of Q where the demand function crosses the Q-axis?

• 11

• 0

• 7

• 21.760

Why can't Q be negative in the context of this demand function?

• Because it represents a price

• Because it represents a quantity in thousands

• Because it is a constant

• Because it is a variable

What does a Q value of 21.760 imply about the demand?

• The demand is 217.60 units

• The demand is 21.760 units

• The demand is 21,760 units

• The demand is 2,176 units