Finite Math

Math 120 Your name :__________________________________

Quiz 2

Chapter 2

Define a quadratic equation

Quadratic equation is a polynomial equation of the second degree . The general form is where a ? 0 (if a 0 , then the equation becomes a linear equation

The letters a , b , and c are called coefficients

b is the linear coefficient , since it is the coefficient of x

c is the constant coefficient , also called the free term

x2 - 25 0 can be factored into (x 5 ) and (x - 5

What are the two solutions to

the equation

The solutions can easily be obtained from factors of the equation .If we can 't factor an equation , one thing we can always do is use the quadratic formula . Use this formula to solve

where a , b , and c coefficients are as stated in first question

Thus , the solutions for the equation are 4 . Quadratic equations are parabolas when graphed on the usual Cartesian coordinate system . Sketch the graph of the following equation (You can do this by hand or use excel or a graphing calculator

5 . What are the zeros of the above equation . That is , where does the function cross the x-axis

Saying this another way : solve .It can be seen that , results match the graph

6 . Demand function : y 0 .0095x2 - 1 .9524x 100

Supply function : y 0 .0333x2 20

Find the point of market equilibrium (where the curves cross The curves cross at

0 .0095x2 - 1 .9524x 100 0 .0333x2 20

0 .0095x2 - 0 .0333x2 - 1 .9524x 100 - 20 0

- 0 .0238x2 - 1 .9524x 80 0 Thus , x1 -112 .036 and x2 30

The point of market equilibrium can not be negative , therefore it is at x 30

You have determined that your profit on a particular product line can be described by the equation

How many units should you sell to produce maximum profit (Hint : find the vertex

How much profit would you make if you sold the units determined in part-a

Extra credit : Where do you break even

The vertex can be found using the following formula Therefore , we need to sell 105 units to maximize profit

We can calculate the profit at x 105

Break-even point shows the sales , when the revenues equal expenses . In other words , it means that at break-even point profits equal to zero Therefore

The roots of this equation are : x1 73 and x2 137

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