Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 2-5 GRAPHS OF EXPENSE AND REVENUE FUNCTIONS Write, graph and interpret the expense

Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 1

2-5GRAPHS OF EXPENSE AND REVENUE FUNCTIONS

2-5GRAPHS OF EXPENSE AND REVENUE FUNCTIONS

Write, graph and interpret the expense function. Write, graph and interpret the revenue function.Identify the points of intersection of the expense and revenue functions.

Identify breakeven points, and explain them in the context of the problem.

OBJECTIVES

Financial Algebra© 2011 Cengage Learning. All Rights Reserved.

Warm-UpWarm-Up

Find the vertex of the parabola with equation

Slide 2

1582 xxy


nonlinear function - revenue function - not a straight line.

second-degree equation - function has a variable raised to an exponent of 2

quadratic equation – 2nd degree equation

parabola - The graph of a quadratic equation

leading coefficient - a, in the quadratic equation

maximum value – parabola’s peak

vertex of a parabola – the point at the maximum value

axis of symmetry - vertical line that can be drawn through the vertex of the parabola so that the dissected parts of the parabola are mirror images of each other

Key Terms


Skills and StrategiesSkills and Strategies

Quadratic Equationy = ax2 + bx + c where a, b, and c are real numbers

and a ≠ 0a positive – opens upa negative - opens downaxis of symmetry determined by calculating

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

Slide 4

a

b

2





Parabola with a positive leading coefficient

Parabola with a positive leading coefficient


Parabola with a negative leading coefficient

Parabola with a negative leading coefficient


Example 1Example 1

A particular item in the Picasso Paints product line costs $7.00 each to manufacture. The fixed costs are $28,000. The demand function is q = –500p + 30,000 where q is the quantity the public will buy given the price, p. Graph the expense function in terms of price on the coordinate plane.


An electronics company manufactures earphones for portable music devices. Each earphone costs $5 to manufacture. Fixed costs are $20,000. The demand function is q = –200p + 40,000. Write the expense function in terms of q and determine a suitable viewing window for that function. Graph the expense function.

CHECK YOUR UNDERSTANDING


Example 2Example 2

What is the revenue equation for the Picasso Paints product? Write the revenue equation in terms of the price.


Determine the revenue if the price per item is set at $25.00.



EXAMPLE 3EXAMPLE 3

Graph the revenue equation on a coordinate plane.


Use the graph in Example 3. Which price would yield the higher revenue, $28 or $40?



The revenue and expense functions are graphed on the same set of axes. The points of intersection are labeled A and B. Explain what is happening at those two points.

EXAMPLE 4EXAMPLE 4


Why is using the prices of $7.50 and $61.00 not in the best interest of the company?



ApplicationsApplications

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Slide 15

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Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 2-5 GRAPHS OF EXPENSE AND REVENUE FUNCTIONS Write, graph and interpret the expense