Financial Applications of Quadratic Functions
For problems involving quadratics in finance, it is useful to graph the equation. From these, one can easily find critical values of the function by inspection.
Learning Objective

Apply the quadratic function to real world financial models
Key Points
 In some financial math problems, several key points on a quadratic function are desired, so 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
The method of graphing a function to determine general properties can be used to solve financial problems.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.
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 breakeven points (
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: Visualizing Domain and Range, The Vertical Line Test, and Solving Differential Equations
 graph
 Appears in these related concepts: Graphical Representations of Functions, Graphing Equations, and Reading Points on a Graph
 maximum
 Appears in these related concepts: Relative Minima and Maxima, The Rule of Signs, and Experimental Probabilities
 point
 Appears in these related concepts: Graphing Quadratic Equations In Standard Form, The Intermediate Value Theorem, and Polynomial and Rational Functions as Models
 product
 Appears in these related concepts: Measuring Reaction Rates, Writing Chemical Equations, and Basic Operations
 quadratic
 Appears in these related concepts: The Discriminant, Stretching and Shrinking, and What is a Quadratic Function?
 quadratic function
 Appears in these related concepts: Other Equations in Quadratic Form, Scientific Applications of Quadratic Functions, and Standard Form and Completing the Square
 yintercept
 Appears in these related concepts: SlopeIntercept Equations, Zeroes of Linear Functions, and Linear Equations in Standard Form
Sources
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