Try It!   Scenario #1

Suppose that you run a Music Store and the revenue in thousands of dollars from the sale of n  thousand  CDs  is  given by .   If the cost in thousands of dollars, of producing  n thousand  CDs is given by , how many CDs do you need to sell in order to break even?

Try It!  Scenario #2

Suppose to celebrate the grand opening of your music store, you hire someone to set off a fireworks display from the 80 foot high roof top of the store with an initial velocity of 64 feet per second.  The height of a display t seconds after having been launched is given by Height = .  When will the cardboard shell from the fireworks reach the ground?

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In both of the above situations, two quantities are changing.  What are these  “variables” for each scenario?

            First scenario:

         Second scenario:

Usually, when we have two variables like this, we can think of one being dependent upon the other.  In each of the two scenarios above, which of the two variables depends upon the other?  We call this variable the dependent, or output variable.  The other is the independent, or input variable. Identify the dependent and independent variable in each of the above scenarios.

            First scenario:  dependent:

                                    Independent:

         Second scenario: dependent:

                                    Independent:

Think of three other scenarios that have inputs and outputs.    Identify the independent and dependent variables in each.

The two scenarios about the music store each have a highest power of 2.  We call this type of equation a quadratic.  The word quadratic comes from the Latin word for “square.”   As a matter of fact, we might think of solving a quadratic equation as finding the side of a square with a given area.  For example, to solve , we might ask,  “What is the side of the square whose area is 9?”

                                            9

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