2-5
GRAPHS OF EXPENSE AND
REVENUE FUNCTIONS
Warm Ups:
Find the vertex of the parabola with
equation y = x2 + 8x + 15.
Vertex formula: (-b/2a, y)
Slide 1
Financial Algebra
© Cengage/South-Western
2-5
GRAPHS OF EXPENSE AND
REVENUE FUNCTIONS
OBJECTIVES
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.
Slide 2
Financial Algebra
© Cengage/South-Western
Key Terms
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Slide 3
nonlinear function
second-degree equation
quadratic equation
parabola
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leading coefficient
maximum value
vertex of a parabola
axis of symmetry
Financial Algebra
© Cengage Learning/South-Western
 Nonlinear function - A function that has a graph that is not a straight
line.
 Second-degree equation - A function with a variable raised to an
exponent of 2.
 Quadratic equation - An equation written in the form y = ax2 + bx + c
where a, b, and c are real numbers and a ≠ 0.
 Parabola - The shape of the graph of a quadratic function.
 Leading coefficient - The first coefficient in a quadratic equation when
written in standard form, usually denoted by a.
 Maximum value - The peak or vertex of a parabola; the point where
revenue can be maximized.
 Vertex of a parabola - The peak of the parabola and the point where
revenue is maximized; the point of maximum value in a quadratic
equation.
 Axis of symmetry - A vertical line that can be drawn through the vertex
of a parabola so that the dissected parts of the parabola are mirror
images of each other.
Financial Algebra
Slide 4
© Cengage Learning/South-Western
How can expense and revenue be
graphed?
How does price contribute to consumer
demand?
Name some other factors that might also play a
role in the quantity of a product consumers
purchase.
Why does a non-vertical line have slope but a
nonlinear function does not?
Slide 5
Financial Algebra
© Cengage Learning/South-Western
Parabola with a positive leading
coefficient
Slide 6
Financial Algebra
© Cengage Learning/South-Western
Parabola with a negative leading
coefficient
Slide 7
Financial Algebra
© Cengage Learning/South-Western
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 = –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.
Slide 8
Financial Algebra
© Cengage Learning/South-Western
CHECK YOUR UNDERSTANDING
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.
Slide 9
Financial Algebra
© Cengage Learning/South-Western
Example 2
What is the revenue equation for the Picasso Paints
product? Write the revenue equation in terms of the
price.
Slide 10
Financial Algebra
© Cengage Learning/South-Western
CHECK YOUR UNDERSTANDING
Determine the revenue if the price per item is set at
$25.00.
Slide 11
Financial Algebra
© Cengage Learning/South-Western
EXAMPLE 3
Graph the revenue equation on a coordinate plane.
Slide 12
Financial Algebra
© Cengage Learning/South-Western
CHECK YOUR UNDERSTANDING
Use the graph in Example 3. Which price would yield
the higher revenue, $28 or $40?
Slide 13
Financial Algebra
© Cengage Learning/South-Western
EXAMPLE 4
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.
Slide 14
Financial Algebra
© Cengage Learning/South-Western
CHECK YOUR UNDERSTANDING
Why is using the prices of $7.50 and $61.00 not in the
best interest of the company?
Slide 15
Financial Algebra
© Cengage Learning/South-Western