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Financial Applications of Quadratic Functions
Graphs display complete pictures of quadratic functions and from them one can easily find critical values of the function by inspection.
Learning Objective

Apply the quadratic function to real world financial models
Key Points
 If several key points on a function are desired, it can become tedious to calculate each algebraically.
 Rather than calculating each key point of a function, one can find these values by inspection of its graph.
 Graphs of quadratic functions can be used to find key points in many different relationships, from finance to science and beyond.
Full Text
Given the algebraic equation for a quadratic function, one can calculate any point on the function, including critical values like minimum/maximum and x and yintercepts.
These calculations can be more tedious than is necessary, however. A graph contains all the above critical points and more, and acts as a clear and concise representation of a function. If one needs to determine several values on a quadratic function, glancing at a graph is quicker than calculating several points. This method is often utilized in the financial sector.
As an example, consider the function:
Suppose this models a profit function
If a financier wanted to find the number of sales required to break even, the maximum possible loss (and the number of sales required for this loss), and the maximum profit (and the number of sales required for this profit), they could simply reference a graph instead of calculating it out algebraically.
Financial Example
Graph of the equation
By inspection, we can find that the maximum loss is
Assign just this concept or entire chapters to your class for free.
Key Term Reference
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 function
 Appears in these related concepts: Solving Differential Equations, Visualizing Domain and Range, and The Vertical Line Test
 graph
 Appears in these related concepts: Reading Points on a Graph, Graphing Equations, and Graphical Representations of Functions
 maximum
 Appears in these related concepts: Experimental Probabilities, Relative Minima and Maxima, and The Rule of Signs
 point
 Appears in these related concepts: The Intermediate Value Theorem, Graphing Quadratic Equations In Standard Form, and Polynomial and Rational Functions as Models
 product
 Appears in these related concepts: Writing Chemical Equations, Measuring Reaction Rates, and The State of Competition
 quadratic
 Appears in these related concepts: Stretching and Shrinking, The Discriminant, and What is a Quadratic Function?
 quadratic function
 Appears in these related concepts: Standard Form and Completing the Square, Other Equations in Quadratic Form, and Scientific Applications of Quadratic Functions
 yintercept
 Appears in these related concepts: Zeroes of Linear Functions, SlopeIntercept Equations, and Linear Equations in Standard Form
Sources
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Cite This Source
Source: Boundless. “Financial Applications of Quadratic Functions.” Boundless Algebra. Boundless, 23 Jun. 2016. Retrieved 25 Jul. 2016 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/quadraticfunctionsandfactoring6/applicationsofquadraticfunctions46/financialapplicationsofquadraticfunctions1356111/