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

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 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

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Skills and Strategies Quadratic Equation y = ax 2 + bx + c where a, b, and c are real numbers and a ≠ 0 a positive – opens up a negative - opens down axis of symmetry determined by calculating ph_Calculator/graphCalc.html ph_Calculator/graphCalc.html Slide 4

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5 Parabola with a positive leading coefficient

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 6 Parabola with a negative leading coefficient

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 Example 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 = –500 p + 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.

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 8 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 = –200 p + 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

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 9 Example 2 What is the revenue equation for the Picasso Paints product? Write the revenue equation in terms of the price.

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 10 Determine the revenue if the price per item is set at $ CHECK YOUR UNDERSTANDING

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 11 EXAMPLE 3 Graph the revenue equation on a coordinate plane.

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 12 Use the graph in Example 3. Which price would yield the higher revenue, $28 or $40? CHECK YOUR UNDERSTANDING

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 13 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 4

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 14 Why is using the prices of $7.50 and $61.00 not in the best interest of the company? CHECK YOUR UNDERSTANDING

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. ApplicationsApplications Page 90, #2 - 3 Slide 15