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Overview
Foundations of Mathematics 12 (MAT621A)
Relations and Functions
6. Represent data using polynomial functions of degree ≤ 3 to solve problems
6.4 Applications of polynomial functions
Applications of Polynomial Functions
Polynomials model real quantities like area, volume, and revenue -- with the same tools you already know.
What You'll Learn
Polynomials model real quantities: area, volume, revenue, and projectile height.
Worked example: folding a cut sheet into a box gives volume V(x)=x(20-2x)(12-2x).
The box volume is a cubic polynomial in the cut length x.
Revenue (price times quantity) and projectile height are common polynomial models too.
Once a scenario is a polynomial, the usual factoring and graphing tools apply directly.
What You'll Practice
1
Creating volume formulas from geometric constraints with cut-out dimensions
2
Graphing polynomial functions and identifying realistic domain restrictions
3
Finding maximum values and corresponding x-values using calculator tools
4
Solving age-based word problems by assigning variables and setting up equations
Why This Matters
Polynomial functions model countless real-world situations, from engineering design and manufacturing to financial planning and population growth. Mastering these applications develops your problem-solving skills and prepares you for advanced math, science, and business courses where optimization and modeling are essential.
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Polynomial Functions
Word Problems
Volume Calculations
Domain and Range
Optimization
Graphing
Variable Assignment
Real-World Modeling
PEI Curriculum Aligned