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

Demonstrate how the graphs of quadratic functions can be used to model relationships in the finance and science world
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.
Term

pH
A measurement of a the acidity of a solution, calculated by log[H+], where [H+] is the concentration of H+ ions in the solution.
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 is essentially 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.
Consider the function:
Suppose this models the profit (f(x)) in dollars that a company earns as a function of the number of products (x) of a given type that are sold, and is valid for values of x greater than or equal to 0 and less than or equal to 500.
If one 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), one could calculate algebraically or simply reference a graph.
Interactive Graph: Profit vs. Sales
Graph of quadratic equation
By inspection, we can find that the maximum loss is $750, which is lost at both 0 and 500 sales. Maximum profit is $5500, which is achieved at 250 sales. The breakeven points are between 15 and 16 sales, and between 484 and 485 sales.
The above example pertained to business sales and profits, but a similar model can be used for many other relationships in finance, science and otherwise. For example, the reproduction rate of a strand of bacteria can be modeled as a function of differing temperature or pH using a quadratic functionality.
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Key Term Reference
 equation
 Appears in these related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 function
 Appears in these related concepts: Inverse Functions, Solving Differential Equations, and Functions and Their Notation
 graph
 Appears in these related concepts: Graphing on Computers and Calculators, Reading Points on a Graph, and Graphing 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, Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is not Equal to 0, and Graphing Equations
 quadratic
 Appears in these related concepts: Solving Quadratic Equations by Factoring, The Discriminant, and Quadratic Functions of the Form f(x) = a(xh)^2 + k
 quadratic function
 Appears in these related concepts: Standard Form and Completing the Square, Stretching and Shrinking, and Quadratic Equations and Quadratic Functions
 yintercept
 Appears in these related concepts: Zeroes of Linear Functions, Direct Variation, and SlopeIntercept Equations
Sources
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Cite This Source
Source: Boundless. “Applications.” Boundless Algebra. Boundless, 21 Jul. 2015. Retrieved 01 Sep. 2015 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/functionsequationsandinequalities3/graphsofquadraticfunctions25/applications1356111/