MTH108 Business Math I Lecture 14. Chapter 5 Quadratic and Polynomial Functions.

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Presentation transcript:

MTH108 Business Math I Lecture 14

Chapter 5 Quadratic and Polynomial Functions

Review Need of nonlinear functions Quadratic functions Graphical representation  Parabola; concavity; concave up; concave down; vertex; axis of symmetry; intercepts To find the  Concavity  y-intercept  x-intercept; factorisation, quadratic formula  Vertex ; Axis of symmetry; Symmetry

Today’s Topic Solving real world phenomenon using quadratic functions Sketching the parabolas for these phenomenon

Review

Consider the figure which shows the increase in the average player’s salary of cricket players. Approximate the salary data by using a quadratic function.

For the years 1981, 1985 and 1988, the average player salaries were 190,000, 310,000 and 600,000, respectively. Using these data points, we want to determine the quadratic function which can be used to estimate average player salaries over time. In particular,

Use this function to estimate the average salary in 1995

Determine the equation of the quadratic function which passes through the points

Determine the equation of quadratic function which passes through the points

A survey taken during 1990 indicated the increased availability of computers in public school classrooms.

During the academic year, the no. of students per computer was 125. For the academic year, the no. of students had dropped to For the academic year, the no. was 22 students per computer. Using these three data points, determine the quadratic estimating function.

Applications of quadratic functions Quadratic Revenue Function Suppose that the demand function for the product is Total revenue R from selling q units of price p is

Since the demand function q is stated in terms of price p, total revenue function will be:

Given the p-intercept, what is the value of p maximizes R? What is the max. value? How many units would be demanded at this price?

Quadratic supply function Market surveys of suppliers of a particular product have resulted in the conclusion that the supply function is approximately quadratic in form. Suppliers were asked what quantities they would be willing to supply at different market prices. Results of the survey indicated that at market prices of 25, 30 and 40 dollars, the quantities which suppliers would be willing to offer to the market were 112.5, 250 and 600 units, respectively.

We can determine the equation of the quadratic supply function